## Converting percents into fractions and decimals

### Percent to fraction (P -----> F)

Since percent is always a ratio comparing a number to 100, every percent can be written as a fraction over 100. Once written as a fraction over 100, it is customary to write it in simplest form.

Example 1: Convert 60% into a fraction.

Solution: $\large~60\mbox{%}=\frac{60}{100}=\frac{60÷20}{100÷20}=\frac{3}{5}$

Step 1: Write 60% as a fraction over 100.

Step 2: Reduce the fraction by dividing the numerator and denominator by 20.

Example 2: Convert 48% into a fraction.

Solution: $\large~48\mbox{%}=\frac{48}{100}=\frac{48÷4}{100÷4}=\frac{12}{25}$

Step 1: Write 48% as a fraction over 100.

Step 2: Reduce the fraction by dividing the numerator and denominator by 4.

### Percent to decimal (P -----> D)

Remember in the previous lesson we learned to convert a decimal into a percent by moving the decimal two places to the right. To convert a percent into a decimal you move the decimal two places to the left.

Example 3: Convert 60% into a decimal.

Solution: $\large~60\mbox{%}=60.0\mbox{%}=0.60=0.6$

Step 1: Remind yourself that there is a decimal at the end of the 60.

Step 2: Move the decimal two places to the left.

Example 4: Convert 8% into a decimal.

Solution: $\large~8\mbox{%}=8.0\mbox{%}=0.08$

Step 1: Remind yourself that there is a decimal at the end of the 8.

Step 2: Move the decimal two places to the left. One extra zero needs to be added to allow for the decimal to move two spaces.

 Directions: Use the sliders to change the size of the rectangle. Notice the fraction, decimal, and percent change. Practice converting between fractions, decimals, and percents.

# Self-Check

Question 1

Convert 40% into a fraction.

Question 2

Convert 88% into a fraction.

Question 3

Convert 14% into a decimal.