# Year 12 PhysicsSorting out Indices

Remembering what different powers of ten mean is important in physics and the following tables may help:

Going up! Going down!

100 = 1 100 = 1

101 = 10 10-1 = 0.1

102 = 100 10-2 = 0.01

103 = 1000 10-3 = 0.001

104 = 10000 10-4 = 0.0001

105 = 100000 10-5 = 0.00001

106 = 1000000 10-6 = 0.000001

Fractional Indices and fractions:

Useful ones to remember: √x = x1/2 1/x = x-1

# Problems on Indices

1. Express the answer as a number between 1 and 10 multiplied by a power of ten:

1. x = 0.02

2. x = 216

3. x = 2 500 000

4. x = 0.0003489

1. Express the answer as a number only and as a decimal where necessary:

1. x = 6.5 x 106

2. x = 0.24 x 102

3. x = 30.5 x 10-3

4. x = 0.089 x 10-6

## Manipulating indices

Basically there are just four simple rules to remember:

1. If you multiply two numbers the indices of the powers of ten are added, e.g. 105 x 102 = 107

2. If you divide two numbers the indices of the powers of ten are subtracted, e.g. 107 ÷ 102 = 105

3. If you square or raise to any power a power of ten, the indices are multiplied e.g. (103)2 = 106

4. You can only add or subtract numbers raised to the same powers of ten,

E.g. 3 x 102 + 2 x 103 = 0.3 x 103 + 2 x 103 = 2.3 x 103

Try these, and express the answer each time as a number between 1 and 10 multiplied by a power of ten, or just as a power of ten:

1. 102 x 103

2. 10-2 x 103

3. (4 x 104)/(2 x 108)

4. 10-3/10-6

5. (105)3

6. 4 x 102 + 2 x 103