Question

Use the scientific notation, the Laws of exponents, and a calculator to perform the indicated operations. State your answer rounded to the number of significant digits indicated by the given data.

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

Short answer

The required answer is $1.429326\times {10}^{19}$

Step-by-step solution

Step 1. Scientific Notation and exponent rule.

A positive number x is said to be written in scientific notation if it is expressed as follows:

$x=a\times {10}^n\text{where}1\le a<10$ and n is an integer.

Multiplication rule:$a^m{a}^n=a^{m+n}$

Division rule:$\frac{a^m}{a^n}=a^{m-n}$

Step 2. Perform multiplication and division.

Consider the given number$\frac{1.295643\times {10}^9}{(3.610\times {10}^{-17})(2.511\times {10}^6)}$

Simplify the number except factor 10.

$\begin{array}{l}\frac{1.295643\times {10}^9}{3.610\times 2.511\times {10}^{-17}\times {10}^6}=\frac{1.295643\times {10}^9}{9.06471\times {10}^{-17}\times {10}^6}\\ \approx \frac{0.1429326\times {10}^9}{{10}^{-17}\times {10}^6}\end{array}$

Step 3. Use exponent and Scientific Notation rule.

$\begin{array}{l}\frac{1.295643\times {10}^9}{3.610\times 2.511\times {10}^{-17}\times {10}^6}=\frac{0.1429326\times {10}^9}{{10}^{-17}\times {10}^6}\\ =0.1429326\times {10}^{9-(-17+6)}\\ =0.1429326\times {10}^{9-(-11)}\\ =0.1429326\times {10}^{9+11}\\ =0.1429326\times {10}^{20}\end{array}$

Move the decimal point 1 place right to create a new number from 1 up to 10.

Since we moved the decimal to the right, thus, subtract 1 to the exponent.

$\begin{array}{l}\frac{1.295643\times {10}^9}{3.610\times 2.511\times {10}^{-17}\times {10}^6}=1.429326\times {10}^{20-1}\\ =1.429326\times {10}^{19}\end{array}$