Preliminaries
Powers of Ten and Scientific Notation
Since our number system is based on powers of ten, you should understand the notation and how to work with these powers, as follows:
and so on.
and so on.
Multiplying powers of ten
To multiply powers of ten, add the exponents.
Example 1
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 = 102 × 101 = 10(2 + 1) = 103
1,000 × 100 = 103 × 102 = 10(3 + 2) = 105
0.01 × 0.001 = 10–2 × 10–3 = 10[–2 + (–3)] = 10–5
10,000 × 0.01 = 104 × 10–2 = 10[4+ (–2)] = 102
0.0001 × 1,000 = 10–4 × 103 = 10[–4 + 3] = 10–1
Dividing powers of ten
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).
Example 2
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 = 103 ÷ 102 = 10(3 – 2) = 101or 10
100 ÷ 10,000 = 102 ÷ 104 = 10(2 – 4) = 10–2
1 ÷ 0.01 = 100 ÷ 10–2 = 10[0 – (–2)] = 10(0 + 2)= 102
0.001 ÷ 0.01 = 10–3 ÷ 10–2 = 10[–3 – (–2)] = 10(–3 + 2)= 10–1
10,000 ÷ 0.1 = 104 ÷ 10–1 = 10[4 – (–1)] = 10(4 + 1)= 105
