Standard form - AQASmall numbers

Calculations with very big or small numbers can be made easier by converting numbers in and out of standard form.

Part ofMathsNumber

Small numbers

It is useful to look at patterns to try to understand negative indices:

\(10^0 = 1\)

\(10^{-1} = 0.1\)

\(10^{-2} = 0.01\)

\(10^{-3} = 0.001\)

\(10^{-4} = 0.0001\)

\(10^{-5} = 0.00001\)

\(10^{-6} = 0.000001\)

Example

Write 0.0005 in standard form.

0.0005 can be written as \(5 \times 0.0001\).

\(0.0001 = 10^{-4}\)

So \(0.0005 = 5 \times 10^{-4}\)

Question

What is 0.000009 in standard form?

Example

0.03 = \(3 \times 10^{-2}\) because the 3 is 2 places away from the units column.

0.000039 = \(3.9 \times 10^{-5}\) because the 3 is 5 places away from the units column.

Question

What is 0.000059 in standard form?