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Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023
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Chapter 3

Mathematics in Aviation Maintenance

Formula: 0.90 = 90% ; 0.5 = 50% ; 1.25 = 125% ; 0.335 = 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

Formula: numbers: ; 90% = 0.90 ; 50% = 0.50 ; 5% = 0.05 ; 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 by multiplying by 100 as shown earlier.

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

Formula: 5 ; = 5 ÷ 8 = 0.625 = 62.5% ; 8

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 next 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?

Formula: Algebraic 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:

Formula: N 15 ; = ; 80 100 ; To solve for N: N × 100 = 80 × 15 ; N × 100 = 1,200 ; N = 1,200 ÷ 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?

Formula: Algebraic Method: ; N% of 12 rated horsepower = 10.75 actual horsepower ; N% × 12 = 10.75 ; N% = 10.75 ÷ 12 ; N% = 0.8958 ; N = 89.58

Therefore, the motor efficiency is 89.58%.