Chapter SH, Problem 10.21E

To determine

Write the given expression in scientific notation.

Answer to Problem 10.21E

The Scientific notation of the given number is $1.815\times {10}^{-6}$ .

Explanation of Solution

Given:

The given expression is $\left(4.9\times {10}^{-8}\right)÷\left(2.7\times {10}^{-2}\right)$ .

Calculation:

Rewrite the given expression.

  $=\frac{4.9\times {10}^{-8}}{2.7\times {10}^{-2}}$

  $=\frac{4.9}{2.7}\cdot \frac{{10}^{-8}}{{10}^{-2}}$

To divide powers with the same base, subtract the exponents.

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

  $\begin{array}{l}=\frac{4.9}{2.7}\cdot \left({10}^{-8-\left(-2\right)}\right)\\ =\frac{4.9}{2.7}\cdot \left({10}^{-6}\right)\end{array}$

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.

  $=1.815\times {10}^{-6}$

Scientific notation of the expression $=1.815\times {10}^{-6}$

Hence the Scientific notation of the given expression is $1.815\times {10}^{-6}$ .