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Using Exponents with a Base of 10

You've been introduced to exponents now. Scientific notation is one of the most common uses of exponents you will find in life. The are very important if you plan to study science in high school and college. Basically, scientific notation is multiplying small numbers by a value with a base of ten.

(A small number) * 10An exponent

For example, there is something called a mol in chemistry. A mol is made up of 6.02*1023 molecules. When you do calculations in chemistry you will use that value all of the time.

Speed of light? It's about 3*108 meters per second. The real number is 299,792,458. See how much faster it is to write with scientific notation? It's not always the exact number when you use the notation. For your problems, rounding off should be fine.

Remember distance units? With scientific notation, you can write down numbers in the metric system really easily.

millimeter = 1*10-3
meter = 1
kilometer = 1*103 meters

A reminder that when you see a negative exponent it means that it is less than one.

1*10-3 = .001 (we move the decimal point to the left three spaces)
1*103 = 1,000. (we move the decimal point to the right three spaces)
4.6*10-5 = .000046(we move the decimal point to the left five spaces)
8*106 = 8,000,000. (we move the decimal point to the right six spaces)

6.02*1023?
602,000,000,000,000,000,000,000. (twenty-three to the right)

When we go into more detail we'll cover how you add, subtract, multiply, and divide these numbers quickly.

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- Numbernut: More Basic Math
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