Chapter 1.2, Problem 85E

To determine

To perform: the indicated operation and write the result in scientific notation.

Answer to Problem 85E

  $\frac{1.295643\times {10}^9}{\left(3.610\times {10}^{-17}\right)\left(2.511\times {10}^6\right)}=1.429326\times {10}^{19}$

Explanation of Solution

Given information:

Given expression

  $\frac{1.295643\times {10}^9}{\left(3.610\times {10}^{-17}\right)\left(2.511\times {10}^6\right)}$

Concept used:

Scientific notation:

A notation in which a given quantity can be expressed as a number with significant digits required for a specified degree of accuracy and multiplied by 10 to the appropriate power.

Formula used:

Law of exponents:

  $\begin{array}{l}{a}^m\cdot a^n=a^{m+n}\\ \frac{a^m}{a^n}=a^{m-n}\end{array}$

Calculation:

Consider the given expression.

  $\frac{1.295643\times {10}^9}{\left(3.610\times {10}^{-17}\right)\left(2.511\times {10}^6\right)}$

So, the expression can be simplified as

  $\begin{array}{c}\frac{1.295643\times {10}^9}{\left(3.610\times {10}^{-17}\right)\left(2.511\times {10}^6\right)}=\frac{1.295643\times {10}^9}{3.610\times 2.511\times {10}^{-17}\times {10}^6}\\ =\frac{1.295643\times {10}^9}{9.06471\times {10}^{-17+6}}\\ =\frac{1.295643\times {10}^9}{9.06471\times {10}^{-11}}\\ =14.29326\times {10}^{9+11}\\ =14.29326\times {10}^{20}\\ =1.429326\times {10}^{19}\end{array}$

Hence, $\frac{1.295643\times {10}^9}{\left(3.610\times {10}^{-17}\right)\left(2.511\times {10}^6\right)}=1.429326\times {10}^{19}$ .