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