Converting Fractions, Decimals, and Percents

Fractions, decimals, and percents are three different ways to represent the same value. The word percent literally means "per hundred" or "out of 100." Because of this, a percent is simply a special type of fraction where the denominator is always $100$.

For example, $45\%$ means $45$ out of $100$, which can be written as the fraction $\frac{45}{100}$ or the decimal $0.45$.

Converting Between Decimals and Percents

Decimal to Percent: To change a decimal to a percent, multiply by $100$. A quick shortcut is to move the decimal point two places to the right and add a percent sign ($\%)$.

• Example: Convert $0.125$ to a percent. $0.125 \times 100 = 12.5\%$

Percent to Decimal: To change a percent to a decimal, divide by $100$. The shortcut is to remove the percent sign and move the decimal point two places to the left.

• Example: Convert $8\%$ to a decimal. $8 \div 100 = 0.08$

Converting Fractions to Percents

There are two main methods to turn a fraction into a percent.

Method 1: Make the denominator 100 If the denominator can easily be multiplied to become $100$, multiply both the numerator and the denominator by the same number.

• Example: Convert $\frac{3}{25}$ to a percent. $\frac{3 \times 4}{25 \times 4} = \frac{12}{100} = 12\%$

Method 2: Divide to get a decimal If the denominator doesn't easily multiply to $100$, divide the numerator by the denominator to get a decimal, then convert that decimal to a percent.

• Example: Convert $\frac{3}{8}$ to a percent. $3 \div 8 = 0.375$ $0.375 \times 100 = 37.5\%$

Converting Percents to Fractions

To change a percent to a fraction, simply put the percent value over $100$, drop the percent sign, and simplify the fraction to its lowest terms.

• Example: Convert $45\%$ to a fraction in simplest form. $45\% = \frac{45}{100}$ Divide both the top and bottom by their greatest common factor, which is $5$: $\frac{45 \div 5}{100 \div 5} = \frac{9}{20}$

Common Equivalents to Remember

Memorizing a few common fractions and their decimal and percent equivalents will save you a lot of time:

• $\frac{1}{4} = 0.25 = 25\%$
• $\frac{1}{2} = 0.50 = 50\%$
• $\frac{3}{4} = 0.75 = 75\%$
• $\frac{1}{5} = 0.20 = 20\%$
• $\frac{1}{10} = 0.10 = 10\%$