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Chapter 5: Problem 59

For Exercises \(59-66,\) simplify the expressions. $$(0.4)^{2}$$

Short Answer

Expert verified
0.16

Step by step solution

01

Understand the Expression

Identify the expression that needs to be simplified. In this case, it's \(0.4^{2}\).
02

Square the Number

To square the number \(0.4\), multiply it by itself: \(0.4 \times 0.4\).
03

Perform the Multiplication

Calculate the product: \(0.4 \times 0.4 = 0.16\).
04

Verify the Result

Double check your calculation to ensure accuracy. \(0.4 \times 0.4 = 0.16\) is correct.

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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 that number by itself. When you see an expression like \(0.4^{2}\), it essentially instructs you to calculate \(0.4 \times 0.4\). This operation is common in algebra and helps simplify expressions for further calculations. The visual representation is \(0.4\) raised to the power of \(2\), making it easy to remember the function of squaring. When you perform the multiplication as in the example \(0.4 \times 0.4\), the result is \(0.16\). Squaring can be done with whole numbers, fractions, or decimals.

Key points to remember:
  • Squaring means multiplying a number by itself.
  • The notation \(n^{2}\) indicates \(n \times n\).
  • The square of a positive or negative number is always positive.
  • Squaring decimals follows the same steps as whole numbers.
Decimal Multiplication
Multiplying decimals can be straightforward if you follow certain steps. For example, to multiply \(0.4 \times 0.4\), first ignore the decimal points and multiply the numbers as if they were whole: \(4 \times 4 = 16\).
Next, count the total number of decimal places in the factors (in this case, two places).
Finally, place the decimal point in the product so that it has the same number of decimal places as the total counted, resulting in \(0.16\).

Steps for Decimal Multiplication:
  • Ignore the decimal points and multiply as with whole numbers.
  • Count decimal places in all factors.
  • Place the decimal point in the product accordingly.
Remember, accuracy is crucial when working with decimals. Practice helps you become more precise and quicker in performing such calculations.
Verification of Results
It is always a good idea to verify your results to ensure they are accurate. If you've calculated \(0.4 \times 0.4 = 0.16\), double-check your work by redoing the multiplication or using another method. Recalculation can confirm consistency. Using a calculator is another reliable method to verify your result.

Steps for Verification:
  • Redo the multiplication step by step.
  • Use a calculator to cross-check the manual calculation.
  • Consider alternative methods or strategies if available.
Verification helps build confidence and avoids errors in more complex problems or subsequent steps. Making verification a habit ensures accuracy and solidifies your understanding.

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