Chapter SH, Problem 10.15E

To determine

Write the given expression in scientific notation.

Answer to Problem 10.15E

The Scientific notation of the given number is $1.75\times {10}^1$ .

Explanation of Solution

Given:

The given expression is $\frac{1.4\times {10}^4}{8.0\times {10}^2}$ .

Calculation:

Rewrite the given expression.

  $\frac{1.4}{8.0}\cdot \frac{{10}^4}{{10}^2}$

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.

  $\begin{array}{l}=\frac{1.4}{8.0}\cdot \left({10}^{4-2}\right)\\ =\frac{1.4}{8.0}\cdot \left({10}^2\right)\end{array}$

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.

  $\begin{array}{l}=0.175\times {10}^2\\ =1.75\times {10}^1\end{array}$

Scientific notation of the expression $=1.75\times {10}^1$

Hence the Scientific notation of the given expression is $1.75\times {10}^1$ .