Powers of Ten

Since our number system is based on powers of ten, you should understand the notation and how to work with these powers, as follows:

10 0 = 1

10 1 = 10

10 2 = 10 × 10 = 100

10 3 = 10 × 10 × 10 = 1,000

and so on.

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and so on.

To multiply powers of ten, add the exponents.

Multiply the following and leave the answers in powers of ten.

100 × 10

1,000 × 100

0.01 × .001

10,000 × 0.01

0.0001 × 1,000

100 × 10 = 10 2 × 10 1 = 10 (2 + 1) = 10 3

1,000 × 100 = 10 3 × 10 2 = 10 (3 + 2) = 10 5

0.01 × 0.001 = 10 –2 × 10 –3 = 10 [–2 + (–3)] = 10 –5

10,000 × 0.01 = 10 4 × 10 –2 = 10 [4+ (–2)] = 10 2

0.0001 × 1,000 = 10 –4 × 10 3 = 10 [–4 + 3] = 10 –1

To divide powers of 10, subtract the exponents; that is, subtract the exponent of the second number (the divisor) from the exponent of the first number (the dividend).

Divide the following and leave the answers in powers of ten.

1,000 ÷ 100

100 ÷ 10,000

1 ÷ 0.01

0.001 ÷ 0.01

10,000 ÷ 0.1

1,000 ÷ 100 = 10 3 ÷ 10 2 = 10 (3 – 2) = 10 1or 10

100 ÷ 10,000 = 10 2 ÷ 10 4 = 10 (2 – 4) = 10 –2

1 ÷ 0.01 = 10 0 ÷ 10 –2 = 10 [0 – (–2)] = 10 (0 + 2)= 10 2

0.001 ÷ 0.01 = 10 –3 ÷ 10 –2 = 10 [–3 – (–2)] = 10 (–3 + 2)= 10 –1

10,000 ÷ 0.1 = 10 4 ÷ 10 –1 = 10 [4 – (–1)] = 10 (4 + 1)= 10 5