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Significant Digits. By Michelle Lamary and Caitlin Ostrowski. Counting Significant Digit Rules. All non-zero digits are significant (725 , 2, 12) Trapped zeros are significant (101, 2003) Ending zeros are significant only if the decimal point can be seen ( 100. , 1.10, 100, 20 ) - PowerPoint PPT Presentation

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Significant Significant DigitsDigits

By Michelle LamaryBy Michelle Lamary

and and

Caitlin OstrowskiCaitlin Ostrowski

Counting Significant Digit Counting Significant Digit RulesRules

1.1. All non-zero digits are significantAll non-zero digits are significant(725 , 2, 12)(725 , 2, 12)

2.2. Trapped zeros are significantTrapped zeros are significant(101, 2003)(101, 2003)

3.3. Ending zeros are significant only if the Ending zeros are significant only if the decimal point can be seendecimal point can be seen

((100. , 1.10, 100. , 1.10, 100, 20100, 20))

4.4. Leading (beginning) zeros are never Leading (beginning) zeros are never significantsignificant

(0.001, 0.9)(0.001, 0.9)

Example 1Example 1

401700.0900401700.0900

Example 1 - AnswerExample 1 - Answer

440017170000..00990000 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits

Example 1 - AnswerExample 1 - Answer

401700.09401700.090000 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros

Example 1 - AnswerExample 1 - Answer

401700.09401700.090000 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 2 ending zerosRule 3 – 2 ending zeros

Example 1 - AnswerExample 1 - Answer

401700.0900401700.0900 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal

point shownpoint shown

Example 1 - AnswerExample 1 - Answer

401700.0900401700.0900 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal

point shownpoint shown Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros

Example 1 - AnswerExample 1 - Answer

401700.0900401700.0900 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal

point shownpoint shown Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros

10 Significant Digits10 Significant Digits

Example 2Example 2

0.0070500.007050

Example 2 - AnswerExample 2 - Answer

0.000.0077005500 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers

Example 2 - AnswerExample 2 - Answer

0.000.0070570500 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero

Example 2 - AnswerExample 2 - Answer

0.000.0070570500 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero Rule 3 – 1 ending zeroRule 3 – 1 ending zero

Example 2 - AnswerExample 2 - Answer

0.000.0070507050 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal Rule 3 – 1 sig dig ending zero with decimal

point is shownpoint is shown

Example 2 - AnswerExample 2 - Answer

0.000.0070507050 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal Rule 3 – 1 sig dig ending zero with decimal

point is shownpoint is shown Rule 4 – beginning zeros are not significant (3 Rule 4 – beginning zeros are not significant (3

beginning zeros)beginning zeros)

Example 2 - AnswerExample 2 - Answer

0.000.0070507050 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal Rule 3 – 1 sig dig ending zero with decimal

point is shownpoint is shown Rule 4 – beginning zeros are not significant (3 Rule 4 – beginning zeros are not significant (3

beginning zeros)beginning zeros)

4 significant digits 4 significant digits

Example 3Example 3

700.700.

Example 3 - AnswerExample 3 - Answer

770000.. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number

Example 3 - AnswerExample 3 - Answer

770000.. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros

Example 3 - AnswerExample 3 - Answer

770000.. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zerosRule 3 – 2 ending zeros

Example 3 - AnswerExample 3 - Answer

700.700. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal

point shownpoint shown

Example 3 - AnswerExample 3 - Answer

700.700. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal

point shownpoint shown Rule 4 – 0 leading zerosRule 4 – 0 leading zeros

Example 3 - AnswerExample 3 - Answer

700.700. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal

point shownpoint shown Rule 4 – 0 leading zerosRule 4 – 0 leading zeros

3 significant digits3 significant digits

Example 4Example 4

85008500

Example 4 - AnswerExample 4 - Answer

85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers

Example 4 - AnswerExample 4 - Answer

85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros

Example 4 - AnswerExample 4 - Answer

85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 2 ending zerosRule 3 – 2 ending zeros

Example 4 - AnswerExample 4 - Answer

85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal Rule 3 – 0 sig digs (2 ending zeros but decimal

point is NOT shown)point is NOT shown)

Example 4 - AnswerExample 4 - Answer

85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal Rule 3 – 0 sig digs (2 ending zeros but decimal

point is NOT shown)point is NOT shown) Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros

Example 4 - AnswerExample 4 - Answer

85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal Rule 3 – 0 sig digs (2 ending zeros but decimal

point is NOT shown)point is NOT shown) Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros

2 significant digits2 significant digits

Example 5Example 5

8500.8500.

Example 5 - AnswerExample 5 - Answer

85850000.. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits

Example 5 - AnswerExample 5 - Answer

85850000.. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros

Example 5 - AnswerExample 5 - Answer

85850000.. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zerosRule 3 – 2 ending zeros

Example 5 - AnswerExample 5 - Answer

8500.8500. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal

point shownpoint shown

Example 5 - AnswerExample 5 - Answer

8500.8500. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal

point shownpoint shown Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros

Example 5 - AnswerExample 5 - Answer

8500.8500. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal

point shownpoint shown Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros

4 significant digits4 significant digits

Example 6Example 6

0.00000010.0000001

Example 6 - AnswerExample 6 - Answer

0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number

Example 6 - AnswerExample 6 - Answer

0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros

Example 6 - AnswerExample 6 - Answer

0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zerosRule 3 – 0 sig digs ending zeros

Example 6 - AnswerExample 6 - Answer

0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point Rule 3 – 0 sig digs ending zeros (decimal point

is shown)is shown)

Example 6 - AnswerExample 6 - Answer

0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zerosRule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7 Rule 4 – beginning zeros are not significant (7

non significant beginning zeros)non significant beginning zeros)

Example 6 - AnswerExample 6 - Answer

0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zerosRule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7 Rule 4 – beginning zeros are not significant (7

non significant beginning zeros)non significant beginning zeros)

1 significant digit1 significant digit

Example 7 Example 7

200009200009

Example 7 - AnswerExample 7 - Answer

220000000099 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers

Example 7 - AnswerExample 7 - Answer

200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros

Example 7 - AnswerExample 7 - Answer

200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros

Example 7 - AnswerExample 7 - Answer

200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point Rule 3 – 0 sig digs ending zeros (decimal point

NOT shown)NOT shown)

Example 7 - AnswerExample 7 - Answer

200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point Rule 3 – 0 sig digs ending zeros (decimal point

is NOT shown)is NOT shown) Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros

Example 7 - AnswerExample 7 - Answer

200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zerosRule 3 – 0 sig digs ending zeros Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros

6 significant digits6 significant digits

Example 8Example 8

1010

Example 8 - AnswerExample 8 - Answer

1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number

Example 8 - AnswerExample 8 - Answer

1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros

Example 8 - AnswerExample 8 - Answer

1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 1 ending zeroRule 3 – 1 ending zero

Example 8 - AnswerExample 8 - Answer

1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but Rule 3 – 0 sig digs ( 1 ending zero, but

decimal point is NOT shown)decimal point is NOT shown)

Example 8 - AnswerExample 8 - Answer

1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but Rule 3 – 0 sig digs ( 1 ending zero, but

decimal point is NOT shown)decimal point is NOT shown) Rule 4 – 0 leading zerosRule 4 – 0 leading zeros

Example 8 - AnswerExample 8 - Answer

1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but Rule 3 – 0 sig digs ( 1 ending zero, but

decimal point is NOT shown)decimal point is NOT shown) Rule 4 – 0 leading zerosRule 4 – 0 leading zeros

1 significant digit1 significant digit

Example 9 Example 9

1000.0001000.000

Example 9 - AnswerExample 9 - Answer

11000.000000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number

Example 9 - AnswerExample 9 - Answer

11000.000000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros

Example 9 - AnswerExample 9 - Answer

11000.000000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 6 ending zerosRule 3 – 6 ending zeros

Example 9 - AnswerExample 9 - Answer

1000.0001000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal Rule 3 – 6 sig digs ending zeros with decimal

point shownpoint shown

Example 9 - AnswerExample 9 - Answer

1000.0001000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal Rule 3 – 6 sig digs ending zeros with decimal

point shownpoint shown Rule 4 – 0 leading zerosRule 4 – 0 leading zeros

Example 9 - AnswerExample 9 - Answer

1000.0001000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal Rule 3 – 6 sig digs ending zeros with decimal

point shownpoint shown Rule 4 – 0 leading zerosRule 4 – 0 leading zeros

7 significant digits7 significant digits

Example 10Example 10

11361136

Example 10 - AnswerExample 10 - Answer

11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers

Example 10 - AnswerExample 10 - Answer

11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros

Example 10 - AnswerExample 10 - Answer

11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 3 – 0 ending zeros

Example 10 - AnswerExample 10 - Answer

11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros (Decimal point is NOT Rule 3 – 0 ending zeros (Decimal point is NOT

shown)shown)

Example 10 - AnswerExample 10 - Answer

11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zerosRule 3 – 0 ending zeros Rule 4 – 0 leading zerosRule 4 – 0 leading zeros

Example 10 - AnswerExample 10 - Answer

11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zerosRule 3 – 0 ending zeros Rule 4 – 0 leading zerosRule 4 – 0 leading zeros

4 significant digits4 significant digits

Extra PracticeExtra Practice

Extra Practice AnswersExtra Practice Answers

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