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Scientific Notation Section 8.5

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**So we use scientific notation.**

Positive exponents create very large numbers, and negative exponents create very small numbers. It can take a long time to write out numbers like 1,000,000,000,000,000,000,000,000,000 So we use scientific notation.

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**A number is in scientific notation if it is in the form a x 10n **

where n is an integer and ex: x 1017 ex: x 10-12 Note: 43 x 107 is not in scientific notation. Why not? *Because 43 is not between 1 and 10. We should use 4.3 and make the exponent 8 instead of 7.

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**Examples: Convert to standard notation:**

Positive Exponent: Move the decimal 4 places to the right. = 38,000 Negative Exponent: Move the decimal 4 places to the left. = Move the decimal 8 places to the right. = 400,000,000 Move the decimal 6 places to the left. if base is negative, still a negative number. =

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**Examples: Convert to scientific notation:**

5.) 689,000,000 6.89 There are eight digits after the decimal. 6.) 3.4 There are 4 digits before Step 1: Place a decimal point after the first number. Step 2: Count the number of digits on the other side of the new decimal place. Step 3: The number of digits is the exponent. If the original number is a decimal, it is a negative exponent. Step 4: Multiply your number by 10 to that exponent.

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Practice with 8.4 and 8.5 Please don’t write on the worksheets, use a separate piece of paper. Practice 8.5 Choose any 6 problems from #1-12. Choose any 4 problems from #13-24 Practice 8.4 Choose any 8 problems from #1-24. Choose any 6 problems from #37-52.

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**Homework 8.5 (Due at the beginning of next class.)**

Page 388 (1 – 29 odds, 33 – 45 odds)

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**Working with Scientific Notation:**

A positive exponent means the number is big and a negative exponent means the number is small. Each time you increase the exponent by 1, you are multiplying by 10. Multiplying by 10 moves the decimal one place to the right. Each time you decrease the exponent by 1, you are dividing by 10. Dividing by 10 moves the decimal one place to the left.

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