1. 8-2: S CIENTIFIC N OTATION Essential Question: How do you write a number in scientific notation?

2. 8-2: S CIENTIFIC N OTATION A number in scientific notation is written as the product of two factors in the form a x 10 n, where n is an integer and 1 < a < 10 Examples 3.4 x 10 6 5.43 x 10 13 2.1 x 10 -10 Example 1: Recognizing Scientific Notation Is each number written in scientific notation? If not, explain 56.29 x 10 12 No, 56.29 > 10 0.84 x 10 -3 No, 0.84 < 1 6.11 x 10 5 Yes

3. 8-2: S CIENTIFIC N OTATION Your Turn Is each number written in scientific notation? If not, explain 3.47 x 10 -7 52 x 10 4 0.04 x 10 -5 Yes No, 52 > 10 No, 0.04 < 1

4. 8-2: S CIENTIFIC N OTATION 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 10 7

5. 8-2: S CIENTIFIC N OTATION 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

6. 8-2: S CIENTIFIC N OTATION Your Turn Write each number in scientific notation 267,000 46,205,000 0.0000325 0.000000009 2.67 x 10 5 4.6205 x 10 7 3.25 x 10 -5 9.0 x 10 -9

7. 8-2: S CIENTIFIC N OTATION Example 3: Writing a Number in Standard Notation Write each number in standard notation 1.55 x 10 6 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. 8-2: S CIENTIFIC N OTATION Your Turn Write each number in scientific notation 3.2 x 10 12 5.07 x 10 4 5.6 x 10 -4 8.3 x 10 -2 3,200,000,000,000 50,700 0.00056 0.083

9. 8-2: S CIENTIFIC N OTATION 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 10 27 8.7 x 10 25 1.0 x 10 26 5.7 x 10 26 25 is the smallest exponent For the 26 exponents, 1.0 < 5.7 8.7 x 10 25 1.0 x 10 26 5.7 x 10 26 3.7 x 10 27 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

10. 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 10 5 ) = (7 ● 4) x 10 5 = 28 x 10 5 = 2.8 x 10 6 0.5(1.2 x 10 -3 ) = (0.5 ● 1.2) x 10 -3 = 0.6 x 10 -3 = 6.0 x 10 -4

11. 8-2: S CIENTIFIC N OTATION Your Turn Simplify. Write your answer in scientific notation. 2.5(6 x 10 3 ) 1.5 x 10 4 0.4(2 x 10 -9 ) 8 x 10 -10

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