Chapter SH, Problem 10.13E

To determine

Write the given expression in scientific notation.

Answer to Problem 10.13E

The Scientific notation of the given number is $8.51637\times {10}^2$ .

Explanation of Solution

Given:

The given expression is $\left(4.237\times {10}^4\right)\left(2.01\times {10}^{-2}\right)$ .

Calculation:

Rewrite the given expression.

  $\left(4.237\times 2.01\right)\left({10}^4\times {10}^{-2}\right)$

To multiply powers with the same base, add the exponents.

  $a^m\cdot a^n=a^{m+n}$ , where $a\ne 0$ and $m$ and $n$ are rational numbers.

  $\begin{array}{l}=\left(4.237\times 2.01\right)\left({10}^{4-2}\right)\\ =\left(4.237\times 2.01\right)\left({10}^2\right)\end{array}$

Scientific notation $\to$ it is a standard way of writing very large and very small numbers.

The form of the Scientific notation is

  $n\times {10}^m$ , where $1\le n<10$ and $m$ is an integer.

Remove parentheses.

  $=8.51637\times {10}^2$

Scientific notation of the expression $=8.51637\times {10}^2$

Hence the Scientific notation of the given expression is $8.51637\times {10}^2$ .