Data Organization: Background You’ll Need 1

Lumen Learning

Data Organization: Background You’ll Need 1

Convert percents

Percents to Fractions

Percents are a way of expressing ratios or comparisons, where the comparison is to a standard value of 100. The word ‘percent’ itself comes from the Latin “per centum,” which means “by the hundred.” This is why, when we convert a percent to a fraction, the denominator is always [latex]100[/latex] — it represents the ‘whole’ in terms of ‘per hundred’.

How To: Convert a Percent to a Fraction

Write the Percent as a Fraction: Begin by writing the percent as a fraction with the percent number as the numerator and [latex]100[/latex] as the denominator.
Remove the Percent Sign: When you write the percent as a fraction, omit the percent sign since you are now using the fraction format to represent the same value.
Simplify the Fraction: Look for the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number to simplify the fraction.

Convert each percent to a fraction:

[latex]\text{36%}[/latex]
[latex]\text{125%}[/latex]

The previous example shows that a percent can be greater than [latex]1[/latex]. We saw that [latex]\text{125%}[/latex] means [latex]{\Large\frac{125}{100}}[/latex], or [latex]{\Large\frac{5}{4}}[/latex]. These are improper fractions, and their values are greater than one.

Sometimes, percents aren’t whole numbers. They can include decimal points or even be written as a fraction of a percent. To convert these to fractions, you’ll need to adjust the initial fraction before simplifying.

How to: Convert Decimal Percents to Fractions

Write the Decimal Percent as a Fraction: Start by writing the decimal percent as a fraction with the decimal part as the numerator and [latex]100[/latex] as the denominator.
Eliminate the Decimal Point: Multiply both the numerator and the denominator by [latex]10[/latex] for each digit after the decimal point to eliminate the decimal.
Simplify the Fraction: Simplify the resulting fraction by finding the greatest common divisor (GCD) and dividing both the numerator and the denominator by this number.

How to: Convert Fractional Percents to Fractions

Convert the Mixed Number to an Improper Fraction: Convert the mixed number into an improper fraction.
Apply the Percent to Fraction Conversion: Now treat this as a regular percent to fraction conversion. Write the improper fraction with [latex]100[/latex] as the denominator.
Simplify the Complex Fraction: Simplify the complex fraction by multiplying by the reciprocal of the denominator.

Convert each percent to a fraction:

[latex]\text{24.5%}[/latex]
[latex]33\Large\frac{1}{3}\normalsize\%[/latex]

Percents to Decimals

Percents and decimals are both ways of expressing ratios and proportions. A percent tells you how many parts out of a hundred, while a decimal expresses parts of a whole divided into ten, hundred, thousand, and so on. Converting a percent to a decimal helps you understand these ratios in a different light and can simplify further calculations.

How To: Convert a Percent to a Decimal

Write the Percent as a Number: Remove the percent symbol (%) from the percent to focus on the number itself.
Write the percent as a ratio: Create a ratio with the number as the numerator and the denominator as [latex]100[/latex].
Finalize the Decimal: Convert the fraction to a decimal by dividing the numerator by the denominator.

Convert each percent to a decimal:

[latex]\text{6%}[/latex]
[latex]\text{78%}[/latex]

Convert each percent to a decimal:

[latex]\text{135%}[/latex]
[latex]\text{12.5%}[/latex]

[latex]36\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{36}{100}}[/latex]
Simplify.	[latex]{\Large\frac{9}{25}}[/latex]

[latex]125\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{125}{100}}[/latex]
Simplify.	[latex]{\Large\frac{5}{4}}[/latex]

[latex]24.5\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{24.5}{100}}[/latex]
Clear the decimal by multiplying numerator and denominator by [latex]10[/latex].	[latex]{\Large\frac{24.5\left(10\right)}{100\left(10\right)}}[/latex]
Multiply.	[latex]{\Large\frac{245}{1000}}[/latex]
Rewrite showing common factors.	[latex]{\Large\frac{5\cdot {49}}{5\cdot {200}}}[/latex]
Simplify.	[latex]{\Large\frac{49}{200}}[/latex]

[latex]33\Large\frac{1}{3}\normalsize\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{33\Large\frac{1}{3}}{100}}[/latex]
Write the numerator as an improper fraction.	[latex]{\Large\frac{\frac{100}{3}}{100}}[/latex]
Rewrite as fraction division, replacing [latex]100[/latex] with [latex]\frac{100}{1}[/latex]	[latex]{\Large\frac{100}{3}}\div {\Large\frac{100}{1}}[/latex]
Multiply by the reciprocal.	[latex]{\Large\frac{100}{3}} \cdot {\Large\frac{1}{100}}[/latex]
Simplify.	[latex]{\Large\frac{1}{3}}[/latex]

[latex]6\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\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]{\Large\frac{78}{100}}[/latex]
Change the fraction to a decimal by dividing the numerator by the denominator.	[latex]0.78[/latex]

[latex]135\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\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]{\Large\frac{12.5}{100}}[/latex]
Change the fraction to a decimal by dividing the numerator by the denominator.	[latex]0.125[/latex]