a. 40 parts in 100

b. 40/100

c. 0.40

d. 2/5 (40/100 = 4/10 = 2/5)

B. Converting percents to decimals

1. To convert a percent to a decimal, remove the percent sign and move the decimal point two places to the left.
   
   a. Examples:    58% = 0.58   72% = 0.72

C. Converting decimals to percents

1. To convert a decimal to a percent, move the decimal point two places to the right and add the percent sign.
   
   a. Example:    0.17 = 17%

D. Converting fractions to percents

1. To convert a fraction to a percent, reduce the fraction to a decimal, then move the decimal point two places to the right, and add the percent sign.
   
   a. Example:    1/2 = 0.50 = 50%

E. Expressing a percent as a ratio

1. A ratio is the relationship or comparison of two like quantities.
   
   a. Example: 1/2 expressed as a ratio would be 1:2 or “one part in two parts.” This can also be expressed as:
   
   
   
   (1) a decimal (0.5)
   
   
   
   
   (2) a percent (50%)

II. Ratio and Proportion

A. Proportion

1. A proportion expresses the equality of two ratios or fractions. Most pharmacy calculations can be performed using the principles of ratio and proportion.

B. Basic algebraic expression

1. The simplest algebraic form for a ratio and proportion is: A/B = C/D, or A:B = C:D

C. Solving for an unknown

1. By setting two equal ratios together, you may easily solve for an unknown if you know three of the four terms of the proportion.
   
   a. Example: 3/5 = x/15
   
   
   This can be restated as, “if there are 3 parts in 5 parts, then there are x parts in 15 parts.”
   Cross multiply to get: 5(x) = 45
   Rearrange the equation to:    (x) = 45/5
   Divide to get the solution:   x = 45/5 = 9
   Therefore, 3/5 = 9/15, or “3 parts in 5 parts is equivalent to 9 parts in every 15 parts.”

III. Sample Questions

1. Convert the following problems:

a. 72% = 72/100 = 0.______

b. 0.35 = 35% = ______/100 = 7/______

c. 25% = 25/100 = ______:100

d. 0.182 = ______%

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