Chapter 9.5, Problem 41PPS

To determine

To find: The expression $\left(6.2\times {10}^2\right)\times \left(9.1\times {10}^3\right)$ in scientific and standard form.

Answer to Problem 41PPS

The expression $\left(6.2\times {10}^2\right)\times \left(9.1\times {10}^3\right)$ in scientific and standard form are $5.642\times {10}^6$ and $5642000$ respectively.

Explanation of Solution

Given:

The expression is $\left(6.2\times {10}^2\right)\times \left(9.1\times {10}^3\right)$ .

Calculation:

The given expression $\left(6.2\times {10}^2\right)\times \left(9.1\times {10}^3\right)$ is simplified in scientific form as follows:

  $\begin{array}{c}\left(6.2\times {10}^2\right)\times \left(9.1\times {10}^3\right)=6.2\times 9.1\times {10}^2\times {10}^3\\ =56.42\times {10}^{2+3}\\ =\frac{5642}{100}\times {10}^5\\ =\frac{5642}{1000}\times {10}^5\times 10\\ =5.642\times {10}^{5+1}\\ =5.642\times {10}^6\end{array}$

Therefore, the scientific form is $5.642\times {10}^6$ .

The expression $5.642\times {10}^6$ is simplified in standard form as follows:

  $\begin{array}{c}5.642\times {10}^6=\frac{5642}{1000}\times {10}^6\\ =5642\times {10}^{6-3}\\ =5642\times {10}^3\\ =5642000\end{array}$

Thus, the expression $\left(6.2\times {10}^2\right)\times \left(9.1\times {10}^3\right)$ in scientific and standard form are $5.642\times {10}^6$ and $5642000$ respectively.