Question

Express the number$\mathbf{0}\mathbf{.}\mathbf{000862}$ in scientific notation.

Short answer

The scientific notation of the given number is $\mathbf{8}\mathbf{.}\mathbf{62}\mathbf{\times }{\mathbf{10}}^{-\mathbf{4}}$.

Step-by-step solution

Step 1. Write down the given expression.

The given number is $0.000862$.

Step 2. Expressing the given number in scientific notation.

The number $0.000862$ in scientific notation is expressed as:

$\begin{array}{c}0.000862=\frac{862}{{\left(10\right)}^6}\\ =862\times {\left(10\right)}^{-6}\\ =\frac{862\times {\left(10\right)}^{-6}\times {\left(10\right)}^2}{{\left(10\right)}^2}\mathrm{....}\left(\begin{array}{l}\text{Multiplyand}\\ \text{divideby}{\left(10\right)}^2\end{array}\right)\\ =\frac{862}{{\left(10\right)}^2}\times \frac{{\left(10\right)}^{-6}\times {\left(10\right)}^2}{1}\\ =8.62\times {10}^{-4}\end{array}$

Step 3. Conclusion.

The scientific notation of the given number is $8.62\times {10}^{-4}$.