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

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 x x Example 1: Recognizing Scientific Notation Is each number written in scientific notation? If not, explain x No, > x No, 0.84 < x 10 5 Yes

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

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 x 10 7

8-2: S CIENTIFIC N OTATION Example 2b: Writing a Number in Scientific Notation Write each number in scientific notation 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 x 10 -3

8-2: S CIENTIFIC N OTATION Your Turn Write each number in scientific notation 267,000 46,205, x x x x 10 -9

8-2: S CIENTIFIC N OTATION Example 3: Writing a Number in Standard Notation Write each number in standard notation 1.55 x 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 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

8-2: S CIENTIFIC N OTATION Your Turn Write each number in scientific notation 3.2 x x x x ,200,000,000,000 50,

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 x x x is the smallest exponent For the 26 exponents, 1.0 < x x x x Your Turn: List from least to greatest x x x x x x

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 (1.2 x ) = (0.5 ● 1.2) x = 0.6 x = 6.0 x 10 -4

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

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