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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: Example: Convert 3.68 × 107 from scientific notation to

standard notation, as follows. To convert from scientific

Formula: notation to standard notation, move the decimal place 7 places to ; the right. 3.68 × 107 = 36,800,000. Another way to think about ; the conversion is 3.68 × 107 = 3.68 × 10,000,000 = 36,800,000. ; Example: Convert 7.1543 × 10-10 from scientific notation ; to standard notation. Move the decimal place 10 places to ; the left: 7.1543 × 10-10 =.00000000071543. Another way ; to think about the conversion is 7.1543 × 10-10 = 7.1543 × ; 0.0000000001 = 0.00000000071543

When converting, remember that large numbers always have positive powers of ten and small numbers always have negative powers of ten. Refer to Figure 3-11 to determine which direction to move the decimal point.

Addition, Subtraction, Multiplication, and Division of Scientific Numbers

To add, subtract, multiply, or divide numbers in scientific notation, change the scientific notation number back to standard notation. Then add, subtract, multiply or divide the standard notation numbers. After the computation, change the final standard notation number back to scientific notation.

Algebra

Algebra is the branch of mathematics that uses letters or symbols to represent variables in formulas and equations.

Formula: For example, in the equation d = v × t, where distance = velocity

× time, the variables are: d, v, and t.

Equations

Algebraic equations are frequently used in aviation to show the relationship between two or more variables. Equations

Formula: normally have an equals sign (=) in the expression. ; Example: The formula A = π × r2 shows the relationship ; between the area of a circle (A) and the length of the radius ; (r) of the circle. The area of a circle is equal to π (3.1416)

times the radius squared. The larger the radius, the larger the area of the circle.

Algebraic Rules

When solving for a variable in an equation, you can add, subtract, multiply, or divide the terms in the equation (you do the same to both sides of the equals sign) to get the variable onto one side of the equals sign.

Examples: Solve the following equations for the value N.

Formula: 3N = 21

To solve for N, divide both sides by 3.

Formula: 3N ÷ 3 = 21 ÷ 3 ; N = 7 ; N + 17 = 59