Question

Express $0.00000000000942$ in standard form.

Answer 1

Re-write in standard form

$0.00000000000942$ has $14$ digits after the decimal.

So, $0.00000000000942$ can be written as,

$$\begin{gathered} =\frac{942}{100000000000000} \\ =\frac{942}{{10}^{14}} \\ =\frac{9.42\times 100}{{10}^{14}} \\ =9.42\times {10}^2\times {10}^{-14} \end{gathered}$$

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

$$\begin{gathered} =9.42\times {10}^{2-14} \\ =9.42\times {10}^{-12} \end{gathered}$$

So, $\mathbf{9}\mathbf{.}\mathbf{42}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{12}}$ is the standard form of $\mathbf{0}\mathbf{.}\mathbf{00000000000942}$