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Year 12 Physics

Sorting out Indices

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

Going up! Going down!

10^{0} = 1 10^{0} = 1

10^{1} = 10 10^{-1} = 0.1

10^{2} = 100 10^{-2} = 0.01

10^{3} = 1000 10^{-3} = 0.001

10^{4} = 10000 10^{-4} = 0.0001

10^{5} = 100000 10^{-5} = 0.00001

10^{6} = 1000000 10^{-6} = 0.000001

__Fractional Indices and fractions:__

Useful ones to remember: √x = x^{1/2} 1/x = x^{-1}

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

x = 0.02

x = 216

x = 2 500 000

x = 0.0003489

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

x = 6.5 x 10

^{6}x = 0.24 x 10

^{2}x = 30.5 x 10

^{-3}x = 0.089 x 10

^{-6}

Basically there are just four simple rules to remember:

If you multiply two numbers the indices of the powers of ten are added, e.g. 10

^{5}x 10^{2}= 10^{7}If you divide two numbers the indices of the powers of ten are subtracted, e.g. 10

^{7}÷ 10^{2}= 10^{5}If you square or raise to any power a power of ten, the indices are multiplied e.g. (10

^{3})^{2}= 10^{6}You can only add or subtract numbers raised to the same powers of ten,

E.g. 3 x 10

^{2}+ 2 x 10^{3}= 0.3 x 10^{3}+ 2 x 10^{3}= 2.3 x 10^{3}

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:

10

^{2}x 10^{3}10

^{-2}x 10^{3}(4 x 10

^{4})/(2 x 10^{8})10

^{-3}/10^{-6}(10

^{5})^{3}4 x 10

^{2}+ 2 x 10^{3}

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