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Metric Notation, Electrical Prefixes, and Powers of 10

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Overview ● Powers of 10 ● Metric Notation & Electrical Prefixes ● Math Operations

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●You will study numerous electrical measurements in electronics. These measurements often involve very large and very small numbers. You will often have to add, subtract, multiply and divide these numbers. It takes quite a bit of time to perform these calculations. For this reason, powers of ten and metric notation are used to simplify calculations. Overview

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Powers of Ten 4 X 10 3 Exponent Base Number Coefficient A number multiplied by the power of ten Always 10 in the decimal number system Number that shows how many times the base number is used as a multiplier

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4 X 10 = ● Moving the decimal affects the value of the exponent. ●Decimal moves right—exponent increases ●Decimal moves left—exponent decreases Powers of Ten

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● Moving the decimal affects the value of the exponent. ●Decimal moves right—exponent increases ●Decimal moves left—exponent decreases 4 X 10 = Powers of Ten

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Metric Notation / Electrical Prefixes ● A metric prefix is a group of letters with a specific meaning attached to the beginning of units of measure such as mile, foot, meter, or liter. ■The table below lists powers of ten, metric prefixes and symbols commonly used in electronics.

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Math Operations ●Addition ●Subtraction ●Multiplication ●Division

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Addition and Subtraction ● Rule ● Rule-The exponent values must be the same before adding or subtracting. Example 4 X X X X 10 6

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Addition and Subtraction ● Rule ● Rule-The exponent values must be the same before adding or subtracting. Example 4 X X X X X X 10 6

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Multiplication ● Rule ● Rule- Add the exponent values; then multiply the numeric coefficients. Example 4 X 10 3 X 4 X X 10 9

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Division ● Rule ● Rule- Subtract the exponent values and divide the numeric coefficients. Example 4 X 10 6 ÷ 2 X 10 3

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Division ● Rule ● Rule - Subtract the exponent values and divide the numeric coefficients. Example 4 X 10 6 ÷ 2 X X 10 3

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Summary ●Solving math problems in electronics using very large and small numbers can be difficult and time consuming. Very large and small numbers consist of many digits, often zeros. Anyone who has worked with a lot of zeros knows that mistakes in math are easy to make. Powers of 10 and metric prefixes are shorthand methods for expressing very large and very small numbers. Using this shorthand will allow you to perform calculations with greater accuracy.

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Metric Notation, Electrical Prefixes, and Powers of 10

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