Question

Express $0.00000000837$ in standard form.

Answer 1

Re-write in standard form

$0.00000000837$ has $11$ digits after the decimal.

So, $0.00000000837$ can be written in rational form as,

$$\begin{gathered} =\frac{837}{100000000000} \\ =\frac{837}{{10}^{11}} \\ =\frac{8.37\times 100}{{10}^{11}} \\ =8.37\times {10}^2\times {10}^{-11} \end{gathered}$$

Applying,$\mathbf{}{\mathit{x}}^{\mathbf{a}}\mathbf{\times }{\mathit{x}}^{\mathbf{b}}\mathbf{=}{\mathit{x}}^{\mathbf{a}\mathbf{+}\mathbf{b}}$

$$\begin{gathered} =8.37\times {10}^{2-11} \\ =8.37\times {10}^{-9} \end{gathered}$$

So, $\mathbf{8}\mathbf{.}\mathbf{37}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}$ is the standard form of $\mathbf{0}\mathbf{.}\mathbf{00000000837}$ .