math1003 1.13 - significant digits, accuracy, precision

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MATH1003 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 1.13 Significant Digits, Accuracy, and Precision

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Page 1: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

1.13Significant Digits, Accuracy, and Precision

Page 2: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Goal

To be able to define the concepts of significant digits, accuracy, and precision with respect to numbers.

Page 3: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Significant Digits

“A crowd of 7,000 people had gathered to watch the parade.”

Page 4: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

“They planted 2,124 daffodils this year.”

Significant Digits

Page 5: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

7000 2214The number of important, or “significant,” digits in these

numbers are different.

Significant Digits

Page 6: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

7000 2214In 7000, there is only one significant digit.

Significant Digits

Page 7: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

7000 2214In 7000, there is only one significant digit.

Significant Digits

Page 8: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

7000 2214In 7000, there is only one significant digit.In 2214, there are four significant digits.

Significant Digits

Page 9: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Significant Digits

Page 10: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules

Significant Digits

Page 11: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.

Significant Digits

Page 12: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two

significant digits.

Significant Digits

Page 13: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two

significant digits.❖ Leading 0s are not significant.

Significant Digits

Page 14: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two

significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains

a decimal point.

Significant Digits

Page 15: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

Significant Digits

Page 16: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

527Significant Digits

Page 17: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

527Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

Significant Digits

Page 18: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

527Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

527 has 3 significant digits

Significant Digits

Page 19: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

527Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

527 has 3 significant digits

Significant Digits

Page 20: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

527Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

527 has 3 significant digits

Significant Digits

Page 21: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

527Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

527 has 3 significant digits

Significant Digits

Page 22: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-5,032Significant Digits

Page 23: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-5,032Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

Significant Digits

Page 24: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-5,032Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-5,032 has 4 significant digits

Significant Digits

Page 25: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-5,032Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-5,032 has 4 significant digits

Significant Digits

Page 26: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-5,032Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-5,032 has 4 significant digits

Significant Digits

Page 27: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-5,032Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-5,032 has 4 significant digits

Significant Digits

Page 28: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-5,032Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-5,032 has 4 significant digits

Significant Digits

Page 29: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3.68Significant Digits

Page 30: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3.68Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

Significant Digits

Page 31: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3.68Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3.68 has 3 significant digits

Significant Digits

Page 32: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3.68Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3.68 has 3 significant digits

Significant Digits

Page 33: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3.68Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3.68 has 3 significant digits

Significant Digits

Page 34: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3.68Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3.68 has 3 significant digits

Significant Digits

Page 35: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-0.0019Significant Digits

Page 36: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-0.0019Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

Significant Digits

Page 37: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-0.0019Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-0.0019 has 2 significant digits

Significant Digits

Page 38: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-0.0019Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-0.0019 has 2 significant digits

Significant Digits

Page 39: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-0.0019Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-0.0019 has 2 significant digits

Significant Digits

Page 40: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

15,009Significant Digits

Page 41: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

15,009Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

Significant Digits

Page 42: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

15,009Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

15,009 has 5 significant digits

Significant Digits

Page 43: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

15,009Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

15,009 has 5 significant digits

Significant Digits

Page 44: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

15,009Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

15,009 has 5 significant digits

Significant Digits

Page 45: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

15,009Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

15,009 has 5 significant digits

Significant Digits

Page 46: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

15,009Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

15,009 has 5 significant digits

Significant Digits

Page 47: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

15,009Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

15,009 has 5 significant digits

Significant Digits

Page 48: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

23.004Significant Digits

Page 49: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

23.004Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

Significant Digits

Page 50: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

23.004Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

23.004 has 5 significant digits

Significant Digits

Page 51: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

23.004Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

23.004 has 5 significant digits

Significant Digits

Page 52: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

23.004Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

23.004 has 5 significant digits

Significant Digits

Page 53: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

23.004Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

23.004 has 5 significant digits

Significant Digits

Page 54: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

23.004Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

23.004 has 5 significant digits

Significant Digits

Page 55: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

23.004Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

23.004 has 5 significant digits

Significant Digits

Page 56: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-27,500Significant Digits

Page 57: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-27,500Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

Significant Digits

Page 58: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-27,500Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-27,500 has 3 significant digits

Significant Digits

Page 59: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-27,500Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-27,500 has 3 significant digits

Significant Digits

Page 60: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-27,500Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-27,500 has 3 significant digits

Significant Digits

Page 61: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

-27,500Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

-27,500 has 3 significant digits

Significant Digits

Page 62: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3,000.00Significant Digits

Page 63: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3,000.00Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

Significant Digits

Page 64: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3,000.00Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3,000.00 has 6 significant digits

Significant Digits

Page 65: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3,000.00Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3,000.00 has 6 significant digits

Significant Digits

Page 66: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3,000.00Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3,000.00 has 6 significant digits

Significant Digits

Page 67: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3,000.00Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3,000.00 has 6 significant digits

Significant Digits

Page 68: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3,000.00Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3,000.00 has 6 significant digits

Significant Digits

Page 69: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3,000.00Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3,000.00 has 6 significant digits

Significant Digits

Page 70: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

3,000.00Rules❖ All non-zero digits are significant.❖ Zero (0) is a significant digit if it is between two significant digits.❖ Leading 0s are not significant.❖ Trailing 0s are significant only if the number contains a decimal point.

3,000.00 has 6 significant digits

Significant Digits

Page 71: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Accuracy

Page 72: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

AccuracyDefinitionThe accuracy of a number is the number of significant digits in the number.

Page 73: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

AccuracyDefinitionThe accuracy of a number is the number of significant digits in the number.

3.02

Page 74: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionAccuracy

DefinitionThe accuracy of a number is the number of significant digits in the number.

3.02This number is accurate to 3 significant digits.

Page 75: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionDefinitionThe accuracy of a number is the number of significant digits in the number.

Accuracy

Page 76: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionDefinitionThe accuracy of a number is the number of significant digits in the number.

-1,470

Accuracy

Page 77: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionDefinitionThe accuracy of a number is the number of significant digits in the number.

-1,470This number is accurate to 3 significant digits.

Accuracy

Page 78: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Precision

Page 79: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

PrecisionDefinitionThe precision of a number is the place value of the rightmost significant digit.

Page 80: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

PrecisionDefinitionThe precision of a number is the place value of the rightmost significant digit.

3.02

Page 81: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionPrecision

DefinitionThe precision of a number is the place value of the rightmost significant digit.

3.02This number has a precision of 0.01

Page 82: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionPrecision

DefinitionThe precision of a number is the place value of the rightmost significant digit.

3.02This number has a precision of 0.01

Page 83: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionDefinitionThe precision of a number is the place value of the rightmost significant digit.

-1,470

Precision

Page 84: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionDefinitionThe precision of a number is the place value of the rightmost significant digit.

This number has a precision of 10

-1,470

Precision

Page 85: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionDefinitionThe precision of a number is the place value of the rightmost significant digit.

This number has a precision of 10

-1,470

Precision

Page 86: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionDefinitionThe precision of a number is the place value of the rightmost significant digit.

-0.006043

Precision

Page 87: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionDefinitionThe precision of a number is the place value of the rightmost significant digit.

This number has a precision of 0.000001 or 10-6

-0.006043

Precision

Page 88: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

DefinitionDefinitionThe precision of a number is the place value of the rightmost significant digit.

This number has a precision of 0.000001 or 10-6

-0.006043

Precision

Page 89: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Exercises

Page 90: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Exercises

On Monday, the Canadian dollar was trading against the US dollar at 0.9985

Page 91: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Exercises

On Monday, the Canadian dollar was trading against the US dollar at 0.9985

What is the accuracy and precision of the exchange rate?Accuracy ______ Precision ________________________

Page 92: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On Monday, the Canadian dollar was trading against the US dollar at 0.9985

What is the accuracy and precision of the exchange rate?Accuracy ______ Precision ________________________

Exercises

Page 93: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On Monday, the Canadian dollar was trading against the US dollar at 0.9985

What is the accuracy and precision of the exchange rate?Accuracy ______ Precision ________________________4

Exercises

Page 94: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On Monday, the Canadian dollar was trading against the US dollar at 0.9985

What is the accuracy and precision of the exchange rate?Accuracy ______ Precision ________________________4

Exercises

Page 95: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On Monday, the Canadian dollar was trading against the US dollar at 0.9985

What is the accuracy and precision of the exchange rate?Accuracy ______ Precision ________________________4 .0001 or 10-4

Exercises

Page 96: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Exercises

Page 97: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On this sign, it is posted that the population of Toronto is 2,482,000

Exercises

Page 98: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On this sign, it is posted that the population of Toronto is 2,482,000

What is the accuracy and precision of the polpulation count?Accuracy ______ Precision ________________________

Exercises

Page 99: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On this sign, it is posted that the population of Toronto is 2,482,000

What is the accuracy and precision of the polpulation count?Accuracy ______ Precision ________________________

Exercises

Page 100: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On this sign, it is posted that the population of Toronto is 2,482,000

What is the accuracy and precision of the polpulation count?Accuracy ______ Precision ________________________4

Exercises

Page 101: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On this sign, it is posted that the population of Toronto is 2,482,000

What is the accuracy and precision of the polpulation count?Accuracy ______ Precision ________________________4

Exercises

Page 102: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

On this sign, it is posted that the population of Toronto is 2,482,000

What is the accuracy and precision of the polpulation count?Accuracy ______ Precision ________________________4 1000 or 103

Exercises

Page 103: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Exercises

Page 104: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers

Exercises

Page 105: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers

Exercises

Page 106: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers

Exercises

Page 107: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers

What is the accuracy and precision of the distance?Accuracy ______ Precision ________________________

Exercises

Page 108: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

What is the accuracy and precision of the distance?Accuracy ______ Precision ________________________

The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers

Exercises

Page 109: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

What is the accuracy and precision of the distance?Accuracy ______ Precision ________________________2

The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers

Exercises

Page 110: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

What is the accuracy and precision of the distance?Accuracy ______ Precision ________________________2

The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers

Exercises

Page 111: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

What is the accuracy and precision of the distance?Accuracy ______ Precision ________________________2 100 or 102

The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers

Exercises

Page 112: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Exercises

Page 113: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

In a previous federal election, the percentage of registered voters that voted was 64.9

Exercises

Page 114: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

What is the accuracy and precision of the percentage?Accuracy ______ Precision ________________________

In a previous federal election, the percentage of registered voters that voted was 64.9

Exercises

Page 115: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

What is the accuracy and precision of the percentage?Accuracy ______ Precision ________________________

In a previous federal election, the percentage of registered voters that voted was 64.9

Exercises

Page 116: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

What is the accuracy and precision of the percentage?Accuracy ______ Precision ________________________3

In a previous federal election, the percentage of registered voters that voted was 64.9

Exercises

Page 117: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

What is the accuracy and precision of the percentage?Accuracy ______ Precision ________________________3

In a previous federal election, the percentage of registered voters that voted was 64.9

Exercises

Page 118: Math1003 1.13 - Significant Digits, Accuracy, Precision

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

What is the accuracy and precision of the percentage?Accuracy ______ Precision ________________________3 0.1 or 10-1

In a previous federal election, the percentage of registered voters that voted was 64.9

Exercises