# Percentages

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:

#### 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:

#### 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:

Proportion Method:

#### 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: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: