Chapter 12.5, Problem 42STP

To determine

To find: The scientific notation of $0.0000212$ .

Answer to Problem 42STP

The scientific notation of $0.0000212=2.12\times {10}^{-5}$ .

Explanation of Solution

Given information:

The given number is $0.0000212$ .

Calculation:

Consider the real number

  $\mathrm{0.0000212.........}\left(1\right)$

Let us represent the number $0.0000212$ in scientific notation.

Represent $0.0000212$ in the scientific notation:

The real number $0.0000212$ can also be written in the form of rational number

  $A$ number is of the form of $\frac{p}{q},q\ne 0$ is called rational number.

  $0.0000212=\frac{0.0000212}{1}\mathrm{..........}\left(2\right)$

Multiply numerator and denominator of equation $\left(2\right)$ in the right hand side by $100000$ , then

  $0.0000212=\frac{0.0000212\times 100000}{1\times 100000}$ Simplify.

  $=\frac{2.12}{100000}\mathrm{..........}\left(3\right)$

By the property of algebra $100$ can be written as ${10}^{{}^2}$

So, the number $100000$ can be written as;

  $100000={10}^5$

Put the value $100000={10}^5$ in equation $\left(3\right)$ ,

  $0.0000212=\frac{2.12}{{10}^5}\mathrm{..........}\left(4\right)$

Use the property of algebra, $\frac{a}{b^x}=a\cdot b^{-x}$ in the equation $\left(4\right)$

  $0.0000212=2.12\times {10}^{-5}$

Therefore, the scientific notation of $0.0000212$ is $0.0000212=2.12\times {10}^{-5}$ .