8-2: SCIENTIFIC NOTATIONEssential Question: How do you write a number in scientific notation?

8-2: SCIENTIFIC NOTATION

A number in scientific notation is written as the product of two factors in the form a x 10n, where n is an integer and 1 < a < 10 Examples 3.4 x 106 5.43 x 1013 2.1 x 10-

10

Example 1: Recognizing Scientific Notation Is each number written in scientific notation? If

not, explain 56.29 x 1012 No, 56.29 > 10 0.84 x 10-3 No, 0.84 < 1 6.11 x 105 Yes

8-2: SCIENTIFIC NOTATION

Your Turn Is each number written in scientific notation? If

not, explain 3.47 x 10-7

52 x 104

0.04 x 10-5

YesNo, 52 > 10No, 0.04 < 1

8-2: SCIENTIFIC NOTATION

In scientific notation, you use positive exponents to write numbers greater than 1.

You use negative exponents to write a number between 0 and 1

Example 2a: Writing a Number in Scientific Notation Write each number in scientific notation

56,900,000

Move the decimal point 7 places to the left so that only one non-zero number is in front of the decimal point. 7 becomes the exponent.

5.69 x 107

8-2: SCIENTIFIC NOTATION

Example 2b: Writing a Number in Scientific Notation Write each number in scientific notation

0.00985

Move the decimal point 3 places to the right so that only one non-zero number is in front of the decimal point. -3 becomes the exponent.

9.85 x 10-3

8-2: SCIENTIFIC NOTATION

Your Turn Write each number in scientific notation

267,000 46,205,000 0.0000325 0.000000009

2.67 x 105

4.6205 x 107

3.25 x 10-5

9.0 x 10-9

8-2: SCIENTIFIC NOTATION

Example 3: Writing a Number in Standard Notation Write each number in standard notation

1.55 x 106 1.55

A positive exponent indicates a number greater than 0, so move the decimal point 6 spaces to the right. Use 0’s to fill in the gaps

1,550,000

2 x 10-11 2

A negative exponent indicates a number less than 0, so move the decimal point 11 spaces to the left. Use 0’s to fill in the gaps

0.00000000002

8-2: SCIENTIFIC NOTATION

Your Turn Write each number in scientific notation

3.2 x 1012

5.07 x 104

5.6 x 10-4

8.3 x 10-2

3,200,000,000,000

50,7000.00056

0.083

8-2: SCIENTIFIC NOTATION You can compare and order numbers written in

scientific notation Compare the exponents first If the exponents are tied, compare the decimals

Example 4: List from least to greatest 3.7 x 1027 8.7 x 1025 1.0 x 1026 5.7 x 1026

25 is the smallest exponent For the 26 exponents, 1.0 < 5.7

8.7 x 1025 1.0 x 1026 5.7 x 1026 3.7 x 1027

Your Turn: List from least to greatest 1.6749 x 10-24 9.1096 x 10-28 1.6726 x 10-24

9.1096 x 10-28 1.6726 x 10-24 1.6749 x 10-24

8-2: SCIENTIFIC NOTATION

You can multiply a number that is in scientific notation by another number by multiplying the non-exponent parts, and rewriting if necessary

Example 5: Simplify. Write each answer in scientific notation. 7(4 x 105) = (7 ● 4) x 105

= 28 x 105

= 2.8 x 106

0.5(1.2 x 10-3) = (0.5 ● 1.2) x 10-3

= 0.6 x 10-3

= 6.0 x 10-4

8-2: SCIENTIFIC NOTATION

Your Turn Simplify. Write your answer in scientific notation. 2.5(6 x 103) 1.5 x 104

0.4(2 x 10-9) 8 x 10-10

8-2: SCIENTIFIC NOTATION

Assignment Worksheet #8-2 Problems 1 – 45, odds