General (1-8)

Percentage
Percentage means “parts out of one hundred.” The percentage sign is “%”. Ninety percent is expressed as 90% (= 90 parts out of 100). The decimal 0.90 equals 90⁄100, or 90 out of 100, or 90%.

 

Expressing a Decimal Number as a Percentage

To express a decimal number in percent, move the decimal point two places to the right (adding zeros if necessary) and then affix the percent symbol.

Example: Express the following decimal numbers as a percent:

 

 

.90   = 90%
.5     = 50%
1.25   = 125%
.335    = 33.5%

 

 

Expressing a Percentage as a Decimal Number
Sometimes it may be necessary to express a percentage as a decimal number. To express a percentage as a decimal number, move the decimal point two places to the left and drop the % symbol.

 

For example: Express the following percentages as decimal numbers:

 

90%    = .90
50%    = .50
5%      = .05
150%   = 1.5

 

 

Expressing a Fraction as a Percentage
To express a fraction as a percentage, first change the fraction to a decimal number (by dividing the numerator by the denominator), and then convert the decimal number to a percentage as shown earlier.

Example: Express the fraction 5⁄8 as a percentage.

 

 

 

 

 

Finding a Percentage of a Given Number
This is the most common type of percentage calculation. Here are two methods to solve percentage problems: using algebra or using proportions. Each method is shown below to find a percent of a given number.

Example: In a shipment of 80 wingtip lights, 15% of the lights were defective. How many of the lights were defective?

Algebra Method:

 

                            15% of 80 lights = N (number of defective lights)

                                     0.15 × 80 = N
                                               12 = N

 

 

Therefore, 12 defective lights were in the shipment.
Proportion Method: 

 

 

 

 

 

To solve for N: N × 100 = 80 × 15
                      N × 100 = 1200
                      N = 1200 ÷ 100
                      N = 12
                      or
                      N = (80 × 15) ÷ 100
                      N = 12

 

 

Finding What Percentage one Number Is of Another
Example: A small engine rated at 12 horsepower is found to be delivering only 10.75 horsepower. What is the motor efficiency expressed as a percent? 

 

Algebra Method:
N% of 12 rated horsepower = 10.75 actual horsepower
N% × 12 = 10.75
N% = 10.75 ÷ 12
N% = .8958
N = 89.58

Therefore, the motor efficiency is 89.58%.
Proportion Method:

 

 

 

To solve for N: N × 12 = 10.75 × 100
                      N × 12 = 1075
                      N = 1075 ÷ 12
                      N = 89.58
                      or
                      N = (1075 × 100) ÷ 12
                      N = 89.58

Therefore, the motor efficiency is 89.58%.

 

Finding a Number When a Percentage of It Is Known
Example: Eighty ohms represents 52% of a microphone’s total resistance. Find the total resistance of this microphone.

Algebraic Method:
52% of N = 80 ohms
52% × N = 80
N = 80 ÷ .52
N = 153.846

The total resistance of the microphone is 153.846 ohms.
Proportion Method: 

 

 

 

 

 

Solve for N: N × 52 = 80 × 100
                 N × 52 = 8,000
                 N = 8,000 ÷ 52
                 N = 153.846 ohms
                 or
                 N = (80 × 100) ÷ 52
                 N = 153.846 ohms