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**Scientific notation Express vary large or very small numbers in shorter form**

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**The mass of the Earth is… 5980000000000000000000000 kg**

You could also write 5.98 x 10²⁴ kg

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To write a very large number in scientific notation… move the decimal to the left so it is after the first digit the number of spaces you move the decimal to the left becomes the exponent over your 10.

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**With scientific notation it is more easily expressed as….**

It is inconvenient to express the mass of a proton as a pure decimal..... kg With scientific notation it is more easily expressed as…. x 10⁻²⁷kg

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**To write a very small number in scientific notation…**

….move the decimal to the right so it is after the first digit the number of spaces you move the decimal to the right becomes the negative exponent over your 10.

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**Write each of the following in scientific notation**

kg m m³

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**Write each of the following in scientific notation**

3,109,000,000 kg x 10 m x 10⁻⁵ 139,044,902 m³ x 10⁸

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To convert a number from scientific notation into a decimal remember: Move the decimal the number of spaces equal to the exponent over ten. If it is a positive exponent, move it to the right to make it a large number x 10⁶ = If it is a negative exponent, move it to the left because it is a small number 3.54 x 10⁻⁶ =

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**Write each of these quantities as a decimal**

x 10⁷ x 10⁻¹² 5.67 x 10⁴

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**Write each of these quantities as a decimal**

x 10⁷ m 80,500,000 x 10⁻¹² 5.67 x 10⁴ 56,700

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**When multiplying numbers in scientific notation……**

Multiply the decimals normally Add the exponents of 10 3.0 x 10⁵ · 3.0 x 10⁵ = 9.0 x 10¹⁰

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**When dividing numbers in scientific notation……**

Divide the decimals normally Subtract the denominator’s exponent of 10 from the numerator’s exponent 9.0 x 10⁵ = x 10² 3.0 x 10³

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**When adding or subtracting numbers in scientific notation…. 2**

When adding or subtracting numbers in scientific notation… x 10⁵ x 10³ Both numbers must first have the same exponent of x 10³ x 10³= Then you subtract or add the decimals normally and keep the exponent of 10 the same x 10³ or x 10⁵

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**Of course, most of this will be done on your calculator, but remember…**

You must always put numbers in parentheses if you type them in scientific notation, or use the trick below. Get used to using the 2nd , EE button (3.5 x 10^5) Is the same as 3.5 E 5 and no parentheses are required

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**Perform the following operations**

3 x 10 ⁸ X 2 x 10 ⁻²² = 8 x 10³ / 2 x 10 ⁸ = 1 x 10⁴ x 10² =

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