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.

$(7.2\times {10}^{-9})(1.806\times {10}^{-12})$

Short answer

The required answer is $1.3\times {10}^{-20}$.

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

Step 2. Multiply the number.

Consider the given number$(7.2\times {10}^{-9})(1.806\times {10}^{-12})$

Simplify multiply the numbers$7.2\text{and}1.806$.

$7.2\times 1.806=13.0032$

Step 3. Use exponent and Scientific Notation rule.

$\begin{array}{l}(7.2\times {10}^{-9})(1.806\times {10}^{-12})=13.0032\times ({10}^{-9}\times {10}^{-12})\\ =13.0032\times \left({10}^{-9-12}\right)\\ =13.0032\times {10}^{-21}\end{array}$

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

Since we moved the decimal to the left, thus, add 1 to the exponent.

$\begin{array}{l}(7.2\times {10}^{-9})(1.806\times {10}^{-12})=1.30032\times {10}^{-21+1}\\ =1.30032\times {10}^{-20}\\ \approx 1.3\times {10}^{-20}\end{array}$