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Exponents
| 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1,000
104 = 10 x 10 x 10 x 10 = 10,000
also 101 = 10
and 100 = 1 |
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Look at these examples. The first says 10 to the second power, or 10
squared, is 10 times 10 or 100. Then 10 cubed is 10 times 10 times 10 or 1,000.
Next, 10 to the fourth is 10 times 10 times 10 times 10 or 10,000. Also, 10 to the first
power is simply 10. Less obviously, 10 to the zero power equals one. Note that 10 to any
positive power is just one followed by that number of zeros. |
10-1 = 1 =
0.1
1010-2 = 1 = 1 =
1 = 0.01
102 10x10 100
10-3 = 1 =
1 = 1 = 0.001
103 10x10x10 1,000
10-4 = 1 =
1 = 1 = 0.0001
104 10x10x10x10 10,000 |
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These examples deal with negative exponents. A negative sign in the
exponent means the inverse or reciprocal of the same number without a negative sign. Ten
to the minus one means one over ten (one over ten to the first power)
which is point one (one tenth). Ten to the minus two means one over ten squared or point
zero one (one hundredth). Ten to the minus three means one thousandth, and so forth. When
negative exponents are used as powers of ten, the exponent indicates the number of places
following the decimal point up to and including the one. |
| 104 = 10,000 103
= 1,000
102 = 100
101 = 10
100 =
1
10-1 = 0.1
10-2 =
0.01
10-3 =
0.001
10-4 =
0.0001 |
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These examples (Example 8 in your workbook) summarize the powers of 10 and
shows what they represent in regular decimal numbers, from 10 to the fourth being the same
as 10,000 down to 10 to the minus fourth meaning 1/10,000 or .0001. |
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