Small numbers

Check out the updated revision resources for GCSE Maths: Using standard form to express small numbers, with step-by-step slideshows, quizzes, practice exam questions, and more!

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

\(10^0 = 1\)

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

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

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

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

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

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

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?

This process can also be simplified by considering where the first non-zero digit is compared to the units column.

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.

What is 0.000059 in standard form?