Rules associated with powers of ten are as follows:

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 103W, 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 = 1,000W

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Basic Electrical Theory METRIC SYSTEM AND POWERS OF TEN

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 x 105) (3 x 10-3) = 6 x 102

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

1

10n

1 x 10 n

We can transfer any power of 10 from numerator to denominator, or vice-versa,

simply by changing the sign of the exponent.

Example: To divide 8 x 10-5 by 2 x 10-4, divide the numerical number 8 by

2 = 4, then bring the power of 10, in the denominator, up to the

numerator and change the sign of its exponent, then add the

exponents together:

8x10 5

2x10 4

4x10 5 4 4x10 1

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METRIC SYSTEM AND POWERS OF TEN Basic Electrical Theory

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

TABLE A-6

METRIC PREFIXES EXPRESSED

as POWERS of 10

Metric Prefix Power of 10

mega (M) 106

kilo (k) 103

milli (m) 10-3

micro (μ) 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:

Express 780,000 W in Megohms (MW).

1W = 10-6 MW

780,000 W = 780,000 W x 10-6 = 0.78 MW

Express 4.5 V in millivolts (mV).

1 V = 103 mV

4.5 V = 4.5 x 103 mV = 4500 mV