Basic Electrical Theory

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To use the prefixes listed in Table A-4, divide the value of the unit by the value of the prefix, and then add the prefix to the unit.

TABLE A-4 METRIC PREFIXES USED in ELECTRICITY

 Prefix (letter symbol) Value mega (M) Million 1,000,000 kilo (k) thousand 1,000 milli (m) thousandth 0.001 micro () millionth 0.000,001 nano (n) thousand-millionth 0.000,000,001 Pico (p) million-millionth 0.000,000,000,001

Powers of Ten

Another way to express large and small values is to convert the value to powers of 10. This is a convenient way to express values and keep the units in the basic unit notation, rather than converting from one unit of measure to another unit that may be larger or smaller, as we did in metric prefixes above.

Examples of expressing numbers as power of 10 are shown in Table A-5.

Rules associated with powers of ten are as follows:

Rule 1:  To express numbers larger than 1 as a small number times a power of 10, move the decimal point to the left as many places as desired. Then multiply the number obtained by 10 to a power that is equal to the number of places moved.

Example:          To convert 6,000,000, move the decimal point 6 places to the left (6.000,000), then multiply 6 times 10 raised to a power equal to the number of decimal places moved, obtaining 6 x 106.

6,000,000 = 6 x 106

Rule 2:  To express numbers less than 1 as a whole number times a power of 10, move the decimal point to the right as many places as desired. Then multiply the number obtained by 10 to a negative power that is equal to the number of places moved.

Example:          To convert 0.004A, move the decimal point 3 places to the right (004.), then multiply 4 by 10 raised to a negative power equal to the number of decimal places moved, obtaining 4 x 10-3A.

0.004A = 4 x 10-3A

Rule 3:  To convert a number expressed as a positive power of 10 to a decimal number, move the decimal point to the right as many places as the value of the exponent.

Example:          To convert 1 x 103, move the decimal point 3 places to the right (1000.0), then drop the multiple of power of 10, obtaining 1,000.

1 x 103 = 1,000

Rule 4:  To convert a number expressed as a negative power of 10 to a decimal number, move the decimal point to the left as many places as the value of the exponent.

Example:          To convert 5 x 10-3A, move the decimal point 3 places to the left (0.005), then drop the multiple of the power of 10, obtaining 0.005A.

5 x 10-3A = 0.005A

Rule 5:  To multiply 2 or more numbers expressed as powers of 10, multiply the coefficients to obtain the new coefficient, and add the exponents to obtain the new exponent of 10.

Example:          To multiply 2 x 105 by 3 x 10-3, multiply 2 x 3 to get 6, then add the exponents of the powers of 10, 5 + (-3), to get an exponent of 2, obtaining a product of 6 x 102.

(2 x105) (3 x10-3)=6x102

Rule 6:  To divide powers of 10, use the formula:

Table A-6 shows the metric prefixes expressed as powers of 10.

Metric Prefix Power of 10

 mega (M) 106 kilo (k) 103 milli (m) 10-3 micro () 10-6 nano (n) 10-9 pico (p) 10-12

Electrical units can be expressed in different, but equivalent, units by using prefixes expressed in powers of 10.

Examples: