Question

Express the number$421,000$ in scientific notation.

Short answer

The scientific notation of the given number is $\mathbf{4}\mathbf{.}\mathbf{21}\mathbf{\times }{\mathbf{10}}^5$.

Step-by-step solution

Step 1. Write down the given expression.

The given number is $421,000$.

Step 2. Expressing the given number in scientific notation.

The number $421,000$ in scientific notation is expressed as:

$\begin{array}{c}421,000=421\times 1000\\ =421\times {\left(10\right)}^3\\ =\frac{421\times {\left(10\right)}^3{\left(10\right)}^2}{{\left(10\right)}^2}\mathrm{....}\left(\begin{array}{l}\text{Multiplyand}\\ \text{divideby}{\left(10\right)}^2\end{array}\right)\\ =\frac{421}{{\left(10\right)}^2}\times \frac{{\left(10\right)}^3{\left(10\right)}^2}{1}\\ =4.21\times {10}^5\end{array}$

Step 3. Conclusion.

The scientific notation of the given number is $4.21\times {10}^5$$4.21\times {10}^5$.