Chapter SH, Problem 10.18E

To determine

Write the given expression in scientific notation.

Answer to Problem 10.18E

The Scientific notation of the given number is $3.6\times {10}^{18}$ .

Explanation of Solution

Given:

The given expression is $\left(7.2\times {10}^{11}\right)\left(5\times {10}^6\right)$ .

Calculation:

Rewrite the given expression.

  $\left(7.2\times 5\right)\left({10}^{11}\times {10}^6\right)$

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.

  $\begin{array}{l}=\left(7.2\times 5\right)\left({10}^{11+6}\right)\\ =\left(7.2\times 5\right)\left({10}^{17}\right)\end{array}$

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.

  $\begin{array}{l}=36\times {10}^{17}\\ =3.6\times {10}^{18}\end{array}$

Scientific notation of the expression $=3.6\times {10}^{18}$

Hence the Scientific notation of the given expression is $3.6\times {10}^{18}$ .