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How to Calculate with Scientific Notation


Here, you will take a look at how you do calculations with numbers in scientific notations. It’s a piece of cake. The main idea is to work separately with the power of 10’s and the numbers in front of the powers.

Rule

Multiplication with Scientific Notations

(a 10n) (b 10m) = a 10n b 10m = a b 10n+m

(a 10n) (b 10m) = a 10n b 10m = a b 10n+m

Rule

Division with Scientific Notation

a 10n b 10m = a b 10n 10m = a b 10nm

Example 1

Calculate (4 104) (2 102)

You use the multiplication rule.

(4 104) (2 102) = 4 2 104+2 = 8 106

(4 104) (2 102) = 4 2 104+2 = 8 106

Example 2

Calculate 5 104 3 105

Remember to sort. 5 104 3 105 = 5 3 104+5 = 15 109 = 1.5 10 109 = 1.5 109+1 = 1.5 1010

A value in scientific notation has a number from 1 to 10 multiplied by a power of 10. Since 5 3 =15, you will need to convert 15 to a number between 1 and 10. To do this, write 15 = 1.5 10 (in scientific notations) and repeat once more.

Example 3

Calculate 8 106 4 104

You use the division rule.

8 106 4 104 = 8 4 106 104 = 2 1064 = 2 102 = 200

8 106 4 104 = 8 4 106 104 = 2 1064 = 2 102 = 200

Example 4

Calculate 3 109 6 105 and write in scientific notation

You factorize into two fractions 3 109 6 105 = 3 6 109 105 = 0.5 1095 = 0.5 104 = 5 101 104 = 5 103

A value in scientific notation has a number from 1 to 10 multiplied by a power of 10. You must convert 0.5 to a number between 1 and 10. To do this, write 0.5 = 5 101 (in scientific notation) and repeat once more.

The math master thinking about scientific notation

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How to Convert Scientific Notation to Standard Notation