It is useful to look at patterns to try to understand negative index/indicesShows how many times a number has been multiplied by itself. The plural of index is 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 formA system in which numbers are written as a number greater than 1 and less than 10 multiplied by a power of 10 which may be positive or negative..
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?
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.
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?
\(5.9 \times 10^{-5}\) because the 5 is 5 places away from the units column.