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Scientific Notation

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**What is Scientific Notation?**

Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise.

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**Why use scientific notation?**

For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. Numbers expressed in scientific notation can be used in a computation with far greater ease.

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**Scientific notation consists of two parts:**

A number that is 1 or greater but less than 10 Multiplied by a power of 10 N x 10x

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**Are the following in scientific notation??**

x 10^9 x 104 x 10^-3 x 9.002 x 100 x 10^1 x 102 1.00x 10^56 x 10-23 x 10^-1

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**Are the following in scientific notation??**

x 10^9 No x 104 Yes x 10^-3 x 9.002 x 100 x 10^1 x 102 1.00x 10^56 x 10-23 x 10^-1

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**Changing standard form to scientific notation.**

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**To change standard form to scientific notation…**

Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

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Continued… If the original number was less than 1, then the exponent is negative. If the original number was 10 or greater, then the exponent is positive. If the original number was less than 10 (9.999) but 1 or greater (1 or ), then the exponent is zero (0) which means the number is multiplied by 1. 6 x 100 = 6 (10 to the power of zero equals one)

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**Example 1 Given: 289 800 000 Use: 2.898 (moved 8 places)**

Answer: x 108

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**Example 2 Given: 0.000 567 Use: 5.67 (moved 4 places)**

Answer: 5.67 x 10-4

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**Change each of the following standard form numbers into scientific notation.**

34.903

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**Change each of the following standard form numbers into scientific notation.**

34.903 3.78 x 105 9.34 x 10^-3 9.83 x 10-7 x 10^0 x 101

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**Change each of the following standard form numbers into scientific notation.**

1 039 0.167 12.34

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**Change each of the following standard form numbers into scientific notation.**

1 039 0.167 12.34 x 105 1.039 x 10^3 1.67 x 10-1 x 10^1 1.234 x 101

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**Change each of the following standard form numbers into scientific notation.**

190 0.123 1.00

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**Change each of the following standard form numbers into scientific notation.**

190 0.123 1.00 1.9 x 102 x 10^-3 1.23 x 10-1 1 x 100 x 10^10

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**Changing scientific notation to standard form.**

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**To change scientific notation to standard form…**

Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. For 10^0, just drop the 10^0. (Use zeros to fill in places.)

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Example 3 Given: x 106 Answer: (moved 6 places to the right)

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Example 4 Given: x 10-4 Answer: (moved 4 places to the left)

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**Change each of the following numbers in scientific notation into standard form numbers.**

1.493 x 105 2.908 x 10^-4 x 102 1.333 x 10-1 x 10^7

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**Change each of the following numbers in scientific notation into standard form numbers.**

1.493 x 105 2.908 x 10^-4 x 102 1.333 x 10-1 x 10^7

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**Change each of the following numbers in scientific notation into standard form numbers.**

2.345 x 104 x 100 7.904 x 10^-3 x 10-6 2.309 x 10-2

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**Change each of the following numbers in scientific notation into standard form numbers.**

2.345 x 104 x 100 7.904 x 10^-3 x 10-6 2.309 x 10-2 23 450

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**Change each of the following numbers in scientific notation into standard form numbers.**

5.9 x 10^3 x 10-4 6.66 x 10^1 4.543 x 100 x 10^4

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**Change each of the following numbers in scientific notation into standard form numbers.**

5.9 x 10^3 x 10-4 6.66 x 10^1 4.543 x 100 x 10^4 5 900 66.6 4.543 99 989

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Even More Practice Below is a list of links to games and activities all having to do with scientific notation.

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