example
Convert each percent to a fraction:
ⓐ [latex]\text{36%}[/latex]
ⓑ [latex]\text{125%}[/latex]
Solution
ⓐ |
[latex]36%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{36}{100}[/latex] |
Simplify. |
[latex]\frac{9}{25}[/latex] |
ⓑ |
[latex]125%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{125}{100}[/latex] |
Simplify. |
[latex]\frac{5}{4}[/latex] |
Example
Convert each percent to a fraction:
ⓐ [latex]\text{24.5%}[/latex]
ⓑ [latex]33\frac{1}{3}%[/latex]
Solution
ⓐ |
[latex]24.5%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{24.5}{100}[/latex] |
Clear the decimal by multiplying numerator and denominator by [latex]10[/latex]. |
[latex]\frac{24.5\left(10\right)}{100\left(10\right)}[/latex] |
Multiply. |
[latex]\frac{245}{1000}[/latex] |
Rewrite showing common factors. |
[latex]\frac{5\cdot 49}{5\cdot 200}[/latex] |
Simplify. |
[latex]\frac{49}{200}[/latex] |
ⓑ |
[latex]33\frac{1}{3}%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{33\frac{1}{3}}{100}[/latex] |
Write the numerator as an improper fraction. |
[latex]\frac{\frac{100}{3}}{100}[/latex] |
Rewrite as fraction division, replacing [latex]100[/latex] with [latex]\frac{100}{1}[/latex] . |
[latex]\frac{100}{3}\div \frac{100}{1}[/latex] |
Multiply by the reciprocal. |
[latex]\frac{100}{3}\cdot \frac{1}{100}[/latex] |
Simplify. |
[latex]\frac{1}{3}[/latex] |
example
Convert each percent to a decimal:
ⓐ [latex]\text{6%}[/latex]
ⓑ [latex]\text{78%}[/latex]
Answer:
Solution
Because we want to change to a decimal, we will leave the fractions with denominator [latex]100[/latex] instead of removing common factors.
ⓐ |
[latex]6%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{6}{100}[/latex] |
Change the fraction to a decimal by dividing the numerator by the denominator. |
[latex]0.06[/latex] |
ⓑ |
[latex]78%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{78}{100}[/latex] |
Change the fraction to a decimal by dividing the numerator by the denominator. |
[latex]0.78[/latex] |
example
Convert each percent to a decimal:
ⓐ [latex]\text{135%}[/latex]
ⓑ [latex]\text{12.5%}[/latex]
Solution
ⓐ |
[latex]135%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{135}{100}[/latex] |
Change the fraction to a decimal by dividing the numerator by the denominator. |
[latex]1.35[/latex] |
ⓑ |
[latex]12.5%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{12.5}{100}[/latex] |
Change the fraction to a decimal by dividing the numerator by the denominator. |
[latex]0.125[/latex] |
example
Among a group of business leaders, [latex]\text{77%}[/latex] believe that poor math and science education in the U.S. will lead to higher unemployment rates.
Convert the percent to: ⓐ a fraction ⓑ a decimal
Answer:
Solution
ⓐ |
[latex]77%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{77}{100}[/latex] |
ⓑ |
[latex]\frac{77}{100}[/latex] |
Change the fraction to a decimal by dividing the numerator by the denominator. |
[latex]0.77[/latex] |
Example
There are four suits of cards in a deck of cards—hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is [latex]\text{25%}[/latex]. Convert the percent to:
ⓐ a fraction
ⓑ a decimal
Solution
ⓐ |
[latex]25%[/latex] |
Write as a ratio with denominator [latex]100[/latex]. |
[latex]\frac{25}{100}[/latex] |
Simplify. |
[latex]\frac{1}{4}[/latex] |
ⓑ |
[latex]\frac{1}{4}[/latex] |
Change the fraction to a decimal by dividing the numerator by the denominator. |
[latex]0.25[/latex] |
(credit: Riles32807, Wikimedia Commons)