Chapter SH, Problem 10.14E

To determine

Write the given expression in scientific notation.

Answer to Problem 10.14E

The Scientific notation of the given number is $2.422145\times {10}^2$ .

Explanation of Solution

Given:

The given expression is $\frac{7.0\times {10}^5}{2.89\times {10}^3}$ .

Calculation:

Rewrite the given expression.

  $\frac{7.0}{2.89}\cdot \frac{{10}^5}{{10}^3}$

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.

  $\begin{array}{l}=\frac{7.0}{2.89}\cdot \left({10}^{5-3}\right)\\ =\frac{7.0}{2.89}\cdot \left({10}^2\right)\end{array}$

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.

  $=2.422145\times {10}^2$

Scientific notation of the expression $=2.422145\times {10}^2$

Hence the Scientific notation of the given expression is $2.422145\times {10}^2$ .