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Chapter 5: Problem 60

For Exercises \(59-66,\) simplify the expressions. $$(0.7)^{2}$$

Short Answer

Expert verified
0.49

Step by step solution

01

Understand the Problem

The exercise requires simplification of the expression \( (0.7)^2 \). Simplification means finding the value of the expression.
02

Write the Expression

Start by rewriting the expression: \( (0.7)^2 \)
03

Perform the Squaring

Calculate the square of 0.7. Use the formula for squaring a number: \( (a)^2 = a \cdot a \). Here, \((0.7)^2 = 0.7 \cdot 0.7 \).
04

Multiply the Numbers

Multiply 0.7 by 0.7. \( 0.7 \cdot 0.7 = 0.49 \)
05

Write the Simplified Expression

The simplified expression of \( (0.7)^2 \) is 0.49.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Squaring Numbers
Squaring a number means multiplying the number by itself. For example, squaring 2 gives 4 because \(2 \times 2 = 4\). In our exercise, we had to square 0.7. When we square 0.7, we get \(0.7 \times 0.7 = 0.49\).
Always remember: squaring a number amplifies it by the number itself. Whether the number is a whole number or a decimal, the process remains the same.
Multiplication of Decimals
When multiplying decimals, it helps first to ignore the decimal points and multiply the numbers as if they were whole numbers. For instance, multiplying 0.7 by 0.7 can be thought of as multiplying 7 by 7, which equals 49.
After finding the product of the whole numbers, count the total number of digits to the right of the decimal points in the original numbers (0.7 has 1 digit). That is how many places you should have in the final product. So, 49 becomes 0.49 because we move the decimal two places to the left.
Basic Arithmetic Operations
Basic arithmetic operations form the foundation of math. These operations include addition, subtraction, multiplication, and division.
Multiplication is the operation we used in our exercise. Remember, to multiply, line up the numbers and multiply each digit. In our case, multiplying 0.7 by 0.7 involves understanding the multiplication of digits and then placing the decimal point correctly in the answer.
Practice these operations regularly to build a strong mathematical foundation!

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