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Chapter 7: Problem 80

Write the percent from the circle graph as a decimal and a fraction. Europe: \(10 \%\)

Short Answer

Expert verified
10% is 0.10 as a decimal and \(\frac{1}{10}\) as a fraction.

Step by step solution

01

Convert Percent to Decimal

To convert a percentage to a decimal, divide the percentage by 100. For Europe, the percentage given is 10%. Thus, the decimal form of 10% is calculated as follows: \[ 10\% = \frac{10}{100} = 0.10 \]
02

Convert Percent to Fraction

To convert a percentage to a fraction, write the percentage value over 100 and simplify if necessary. For 10%, the fraction is:\[ 10\% = \frac{10}{100} \]Next, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 10:\[ \frac{10}{100} = \frac{1}{10} \]

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Key Concepts

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

Converting Percentages to Decimals
Whenever you come across a percentage, it's essentially a number out of 100. Therefore, when converting percentages to decimals, you simply divide by 100. This essentially shifts the decimal point two places to the left. For example, if you're given 10%, you would divide by 100 to get:
  • 10% = \( \frac{10}{100} \)
  • Which simplifies to 0.10
This conversion is particularly useful for calculations, allowing you to perform multiplication or division without the complication of percentage signs. Whenever you're in doubt, remember that dividing by 100 will always transform your percentage into a convenient, easy-to-use decimal.
Converting Percentages to Fractions
To convert percentages to fractions, the process begins by recognizing that the percent sign (%) denotes parts per hundred. So, any percentage can be translated directly into a fraction format by simply placing the percentage number over 100. For example, with 10%.
  • Write 10 as the numerator and 100 as the denominator: \( \frac{10}{100} \)
  • This fraction represents the same value as the percentage in a different form
  • This step is crucial before simplifying
Fractions can effectively convey portions and will often require a simplification step to be complete. Thus, once you have converted your percentage into a fraction, consider whether it can be simplified for cleaner presentation and easier understanding.
Simplifying Fractions
Simplifying fractions is the process where the numerator and the denominator are divided by the same number, which is their greatest common divisor (GCD). This step makes fractions simpler and more comprehensible. To illustrate this, consider the fraction derived from 10%: \( \frac{10}{100} \).
  • The greatest common divisor of 10 and 100 is 10
  • Divide both numerator and denominator by 10: \( \frac{10 \div 10}{100 \div 10} = \frac{1}{10} \)
  • This fraction, \( \frac{1}{10} \), is its simplest form
Simplification ensures you have the fraction in its most concise form, making it easier to understand and work with further in calculations or comparisons. Percentages simplified into fractions can often reveal neat and precise proportions.

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Most popular questions from this chapter

Check each answer to see if each makes the proportion a true proportion. If any proportion is not true, solve it to find the correct solution. $$\begin{aligned}&\frac{520}{b}=\frac{65}{100}\\\&\text { Is the base equal to } 800 ?\end{aligned}$$

Solve. 30 is \(6 \%\) of what number?

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Solve. Round to the nearest tenth, if necessary. What number is \(22.3 \%\) of \(53,862 ?\)

Solve. \(20 \%\) of 48 is what number?
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