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Chapter 7: Problem 17

Convert each decimal to a percent. $$1.42$$

Short Answer

Expert verified
The decimal 1.42 is equivalent to 142%.

Step by step solution

01

Understand the Relationship Between Decimals and Percents

A decimal can be easily converted to a percent by multiplying it by 100. This is because a percent represents parts per 100, while a decimal represents parts per 1.
02

Multiply the Decimal by 100

Take the decimal number 1.42 and multiply it by 100 to convert it to a percent. This can be calculated as follows: \[1.42 \times 100 = 142\]
03

Interpret the Result as a Percentage

The result from the multiplication, 142, indicates that the decimal 1.42 is equivalent to 142%. The multiplication of the decimal by 100 reformats it into a percentage form.

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Key Concepts

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

Decimal to Percent Conversion
Converting a decimal to a percent is a straightforward process. To transition from a decimal format to a percent format, you multiply the decimal by 100. This transformation reflects the shift from expressing a value as a part of one whole to expressing it as a part of one hundred. For example, if you have the decimal 1.42, you can convert it to a percent by performing the simple multiplication: \(1.42 \times 100\). The result is 142, meaning 1.42 in decimal form is equal to 142% in percent form. This concept hinges on the understanding that percent means "per hundred," so you're essentially scaling the decimal up to a per hundred basis.
Percent Interpretation
After converting a decimal to a percent, interpreting the percent correctly is crucial. The result gives you a value over 100, representing how many parts out of a hundred the decimal value equates to. For instance, when converting 1.42 to 142%, the 142 tells us that 1.42 is equivalent to 142 of the parts when the whole is divided into 100 parts. This is a crucial concept in understanding the relative size of the decimal compared to a whole when expressed as a percent.
  • 142% means 142 parts out of every 100 parts.
  • A value over 100% indicates that the amount is more than the whole.
  • Understanding percent interpretation helps in grasping ratios, proportions, and comparisons within various scenarios.
Mathematical Multiplication
Multiplication forms the cornerstone of converting decimals to percents. The operation itself involves taking any decimal number and multiplying it by 100 to achieve the percent value. When dealing with the decimal 1.42, the mathematical operation is as follows: multiply 1.42 by 100. Use this understanding to approach similar problems easily:
  • Step 1: Identify the decimal number.
  • Step 2: Perform the multiplication with 100.
  • Step 3: Record the product as the percent.
This process magnifies the decimal to adjust its scale to that of a percent, which is based on a hundred. Multiplying by 100 effectively shifts the decimal point two places to the right, simplifying the calculation to see the result in percent form.

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Most popular questions from this chapter

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