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Chapter 5: Problem 696

In the following exercises, simplify each expression. $$ (0.7)^{2} $$

Short Answer

Expert verified
0.49

Step by step solution

01

Identify the Expression

The given expression to simplify is \[ (0.7)^{2} \]
02

Apply the Definition of Squaring

Squaring a number means multiplying the number by itself. Therefore, we need to calculate \[ 0.7 \times 0.7 \]
03

Perform the Multiplication

To multiply the decimals, we can use long multiplication or a calculator. Let's do the multiplication: \[ 0.7 \times 0.7 = 0.49 \]
04

Simplified Expression

After performing the multiplication, the simplified expression 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 involves multiplying that number by itself. Mathematically, if you have a number 'a', its square is represented as \[ a^2 = a \times a \]. This operation is not limited to whole numbers. You can also square fractions and decimals. For instance, in the given exercise, we squared 0.7 which involved calculating \[ 0.7 \times 0.7 = 0.49 \]. Everyone should really understand that squaring not only applies to positive integers but also to negative numbers and decimals. When you square any negative number 'a', the result is always positive: \[ (-a)^2 = a^2 \]. This is because multiplying two negative numbers gives a positive result.
Decimal Multiplication
Multiplying decimals involves a few careful steps. Here, we multiplied 0.7 by 0.7. First, treat the numbers as whole numbers. Next, ignore the decimal points and multiply the digits as you would with whole numbers. For example, multiply 7 by 7 to get 49. Then, count the total number of decimal places in the original numbers. In this case, there are two decimal places: one in each 0.7. Finally, place the decimal point in your result. So, with two decimal places, 49 becomes 0.49. Practicing these steps helps in perfecting decimal multiplication.
  • Step 1: Ignore decimals, multiply as whole numbers.
  • Step 2: Count decimal places in original numbers.
  • Step 3: Apply decimal places to your result.
Following these steps ensures you understand and correctly perform decimal multiplication.
Mathematical Operations
Mathematical operations like addition, subtraction, multiplication, and division are fundamental when simplifying expressions. Each operation has its own rules and properties. For our exercise, the main operation was multiplication. When simplifying expressions, knowing the order of operations is crucial. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember the order.
Here, squaring is our exponent step while multiplication follows next as per PEMDAS. Simplifying expressions correctly often involves:
  • Understanding the type of operation.
  • Applying the operation accurately.
  • Following the correct order of operations.
Practicing these rules consistently will make mathematical operations feel more intuitive.

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