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Chapter 7: Problem 32

Change the percent to a decimal. $$72 \%$$

Short Answer

Expert verified
72% as a decimal is 0.72.

Step by step solution

01

Understand the concept

Percentage means 'per hundred'. So, 72% means 72 out of 100.
02

Convert percent to a fraction

Write the percent as a fraction where the denominator is 100. Thus, 72% is written as \ \( \frac{72}{100} \).
03

Convert the fraction to a decimal

Divide the numerator by the denominator to convert the fraction \ \( \frac{72}{100} \) to a decimal. \( 72 \div 100 = 0.72 \).

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Key Concepts

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

percentage
A percentage represents a number or a ratio expressed as a fraction of 100. For example, 72% means 72 parts out of 100. Percentages are commonly used to compare quantities, represent probabilities, and understand proportions.

Percent literally means 'per cent' or 'per hundred'. It is denoted by the symbol \(\%\). To think about a percentage, imagine it as slicing something into 100 equal parts.
  • If you have 50 out of these 100 parts, it is 50%.
  • If you have 25 parts, it is 25%.

Understanding percentages is important for many real-life situations, such as calculating discounts, grades, and interest rates.
fraction to decimal conversion
Converting a fraction to a decimal involves division. A fraction is composed of two parts: the numerator (top number) and the denominator (bottom number). To convert into a decimal, you divide the numerator by the denominator.

For example, to convert \(\frac{72}{100}\) into a decimal, you perform the division: \(\frac{72}{100} = 0.72\). This tells you that 72 out of 100 is equal to 0.72 in decimal form.

This method works for any fraction:
  • If your fraction is \(\frac{1}{4}\), divide 1 by 4 to get 0.25.
  • If your fraction is \(\frac{3}{5}\), divide 3 by 5 to get 0.6.

When dealing with fractions and converting them to decimals, practice will make you more comfortable with the process.
decimal representation
Decimals are another way to express fractions and percentages. They are based on the powers of 10. Each position to the right of the decimal point represents a negative power of 10 (tenths, hundredths, thousandths, etc.).

For instance, the number 72% as a fraction is \(\frac{72}{100}\), and as a decimal, it is 0.72. The '7' is in the tenths place, and the '2' is in the hundredths place.

Understanding how to read and write decimals is crucial. Here's why:
  • They provide a clear and precise way to represent numbers that are not whole.
  • Decimals are used in many everyday contexts, including money, measurements, and data calculations.

It's important to be comfortable converting between percentages, fractions, and decimals, as it helps in understanding and comparing different forms of numerical data.

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Most popular questions from this chapter

Solve the equations. $$12 x=48$$

During a 5 -year period, the number of participants collecting food stamps went from 27 million to 17 million. What is the percent decrease? Round to the nearest whole percent.

The yearly deductible for Diane's health-care plan rose from \(\$ 800\) to \(\$ 1000\). What is the percent increase?

If a bank compounds interest quarterly for 2 years, how many total compounding periods are there?

Convert the decimal to a percent. $$1.014$$
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