Chapter 4.1, Problem 1E

To determine

To calculate: The simplified form of the expression ${\left(0.1\right)}^2$ and verify the result with help of calculator.

Answer to Problem 1E

The simplified form of the expression ${\left(0.1\right)}^2$ is $0.01$ .

Explanation of Solution

Given information:

The expression ${\left(0.1\right)}^2$ .

Formula used:

The expression of the form $a^n$ is expressed as $a\cdot a\cdot a\cdot \dots \cdot a\left[n\text{ times}\right]$ where a is the base and n is the exponent.

Calculation:

Consider the expression ${\left(0.1\right)}^2$ .

Recall that the expression of the form $a^n$ is expressed as $a\cdot a\cdot a\cdot \dots \cdot a\left[n\text{ times}\right]$ where a is the base and n is the exponent.

Compare ${\left(0.1\right)}^2$ and $a^n$ . Here a is $\left(0.1\right)$ and n is 2.

Use $\left(0.1\right)$ as a base 2 times,

  ${\left(0.1\right)}^2=\left(0.1\right)\cdot \left(0.1\right)$

Multiply the numbers obtained above,

  $\begin{array}{c}{\left(0.1\right)}^2=\left(0.1\right)\cdot \left(0.1\right)\\ =0.01\end{array}$

Next, use a calculator.

Step 1: Enter the expression $\left(0.1\right)$ .

Step 2: Press the $x^2$ key.

Step 3: Press the $\text{ENTER}$ key.

The value obtained on screen is $0.01$ .

Therefore, it is verified.

Thus, the simplified form of the expression ${\left(0.1\right)}^2$ is $0.01$ .