Metric Notation, Electrical Prefixes, and Powers

of 10

Overview

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

● 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

Powers of Ten

4 X 103

Exponent

Base NumberCoefficientA 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

4 X 10 = 4000.3

1 2 3

● Moving the decimal affects the value of the exponent.● Decimal moves right—exponent increases● Decimal moves left—exponent decreases

Powers of Ten

● Moving the decimal affects the value of the exponent.● Decimal moves right—exponent increases● Decimal moves left—exponent decreases

4 X 10 = 0.004- 3

3 2 1

Powers of Ten

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.

Math Operations

● Addition● Subtraction● Multiplication● Division

Addition and Subtraction

● Rule-The exponent values must be the same before adding or subtracting.

Example

4 X 106

+ 4 X 106

4 X 106

- 2 X 106

Addition and Subtraction

● Rule-The exponent values must be the same before adding or subtracting.

Example

4 X 106

+ 4 X 106

8 X 106

4 X 106

-2 X 106

2 X 106

Multiplication

● Rule- Add the exponent values; then multiply the numeric coefficients.

Example

4 X 103

X 4 X 106

16 X 109

Division

● Rule- Subtract the exponent values and divide the numeric coefficients.

Example

4 X 106

÷ 2 X 103

Division

● Rule- Subtract the exponent values and divide the numeric coefficients.

Example

4 X 106

÷ 2 X 103

2 X 103

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.

Metric Notation, Electrical Prefixes, and Powers

of 10