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Powers of Ten

A power of ten is a power where you have 10 as the base and the exponent is an integer, like this:

10n

If n is larger than 0, you multiply 10 by itself n times. If n is less than 0, you multiply 1 10 by itself n times.

Example 1

Find the power 104 and write it as an ordinary number

104 = 10 × 10 × 10 × 10 = 10000.

Example 2

Calculate the power 103 and write it as an ordinary fraction

103 = 1 103 = 1 10 × 10 × 10 = 1 1000.

Note! In the last example, you see that the power with negative exponent 103 has changed from being above to being below the fraction bar, so the expression becomes 1 103. You put 1 in the denominator as you only have one 103.

Rule

Rules for Powers of Ten

When you work with powers of ten it is good to remember that:

  • when you multiply by 10, you move the decimal mark one place to the right.

  • when you multiply by a power 10n, you move the decimal mark n places to the right.

  • when you divide by 10 (or multiply by 1 10), you move the decimal mark one place to the left.

  • when you multiply by a power 10n, you move the decimal mark n places to the left.

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