Calculations with very big or small numbers can be made easier by converting numbers in and out of standard form.
Part of MathsNumber
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 \(0.0005 = 5 \times 10^{-4}\)
What is 0.000009 in standard form?
0.000009 can be written as \(9 \times 0.000001\).
\(0.000001 = 10^{-6}\)
So: \(0.000009 = 9 \times 10^{-6}\)
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?
\(5.9 \times 10^{-5}\) because the 5 is 5 places away from the units column.