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Scientific Notation

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**Let’s Investigate! 1.) What pattern do you notice?**

6.71 x = 6.71 x = 6.71 x = 6.71 x = 6.71 x = 6.71 x = 6.71 x 1,000,000 = 6,710,000 6.71 x 100,000 = 671,000 6.71 x 10,000 = 67,100 6.71 x 1,000 = 6,710 6.71 x 100 = 671 6.71 x 10 = 67.1 1.) What pattern do you notice? 2.) Multiply x 109 6,710,000,000

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**How wide is our universe?**

210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

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**A number is expressed in scientific notation when it is in the form**

a x 10n where a is between 1 and 10 and n is an integer

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**Write the width of the universe in scientific notation.**

210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

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2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023

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When changing scientific notation to standard notation, the exponent tells you how many places to move the decimal: With a positive exponent, move the decimal to the right: 4.08 x 103 = 4 0 8 Don’t forget to fill in your zeroes!

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**The exponent tells how many spaces to move the decimal:**

In this problem, the exponent is +5, so the decimal moves 5 spaces to the right.

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**Try changing these numbers from Scientific Notation to Standard Notation:**

9.678 x 104 x 103 x 107 x 109 96780 7452.1

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**Standard Notation to Scientific Notation:**

1) First, move the decimal after the first whole number: 2) Second, add your multiplication sign and your base (10). x 10 3) Count how many spaces the decimal moved and this is the exponent. x 10 3 3 2 1

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**Try changing these numbers from Standard Notation to Scientific Notation:**

5673 x 106 x 107 x 109 5.673 x 103

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**Negative Scientific Notation**

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**When using Scientific Notation, there are two kinds of exponents: positive and negative**

Positive Exponent: 2.35 x 108 Negative Exponent: 3.97 x 10 -7

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**Express 0.0000000902 in scientific notation.**

Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10-8

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When changing scientific notation to standard notation, the exponent tells you if you should move the decimal: With a negative exponent, move the decimal to the left: 4.08 x 10-3 = Don’t forget to fill in your zeroes!

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**An easy way to remember this is:**

If an exponent is positive, the number gets larger, so move the decimal to the right. If an exponent is negative, the number gets smaller, so move the decimal to the left.

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**The exponent also tells how many spaces to move the decimal:**

In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

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**When changing from Standard Notation to Scientific Notation:**

4) See if the original number is greater than or less than one. If the number is greater than one, the exponent will be positive. = x 105 If the number is less than one, the exponent will be negative. = 6.72 x 10-8

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