Changing a Percent to a Decimal

Any number written as a percent may be written as a decimal. To change a percent to a decimal, drop the percent symbol and divide by 100.

Example:

Percent Differential

Percent differentials are used to provide a means of comparing changes in quantities or amounts. Percent differentials express the relationship between some initial condition and another specified condition.

The method of calculating percent differential involves the following: Step 1: Subtract the original value from the present value. Step 2: Divide by the original value.

Step 3:Multiply by 100.

Step 4:Add the percent symbol

Example:

A tank initially contains 50 gallons of water. Five gallons are drained out. By what percent is the amount of water in the tank reduced?

Solution:

Step 1:The difference between initial and final is given in the problem: 5 gallons.

Step 2:

Step 3:0.1 x 100 = 10% Five gallons represents 10% of the original 50 gals that were in the tank.

Ratio

Two numbers may be compared by expressing the relative size as the quotient of one number divided by the other and is called a ratio. Ratios are simplified fractions written with a colon (:) instead of a division bar or slash.

Example:

One day Eric paid $700 for a stereo and Scott paid $600 for the same stereo. Compare the amount that Eric paid to the amount that Scott paid, using ratios.

Solution:

Step 1:Divide the numbers to be compared. In this example the amount paid by

Scott is being compared to the amount paid by Eric. The amount paid by

Eric is divided by the amount paid by Scott =

Step 2:Simplifying this expression, both 700 and 600 can be divided by 100.

Step 3:Expressing this fraction as a ratio:

Example:

If one yard equals three feet, what is the ratio of yards to feet? Solution:

Summary

Pertinent information concerning percentages and ratios is summarized below.

Percentages and Ratios Summary

Change decimals to percents by multiplying by 100 and adding the percent symbol.

Change fractions to percents by first changing the fraction into a decimal. Then change the decimal to a percent.

Compute percent differential by dividing the difference by the original value, multiplying by 100, and adding the percent symbol.

Ratios are fractions written with a colon instead of a division bar or slash.