POWERS OF 10




 
A number multiplied by itself is a SQUARED number.

2 x 2 = 4

4 x 4 = 16

2 x 2 and 4 x 4 can be written as

22 = 4

42 = 16

The top 2 is called the INDEX and its value is called the  POWER of the number.

So we say 4 to the power of 2 = 16.
 
 

 
 
Most commonly in electronics we use powers of the number 10.

The 10 is known as the BASE.

102 = 10 x 10 = 100 (base 10 to the power of 2)

103 = 10 x 10 x 10 = 1000 (base 10 to the power of 3)

The power shows how many times 10 is multiplied by itself.

 
We can make large numbers more compact by using powers.

10,000,000 = 107

1,000,000 = 106

1000 = 103

100 = 102

10 = 101  (usually written 10).

Note that the index is the same as the number of zeros (but only for base 10)

1 = 100

0.1 = 10-1

0.01 = 10-2

etc

 
 
Developing this

40,000 = 4 x 104 (4 times 10 to the power of 4)

300 = 3 x 102

44,000 = 44 x 103

0.04 = 4 x 10-2

0.003 = 3 x 10-3

To multiply two numbers with the same base but different powers such as

53 x 52

Simply add the powers.

53+2 = 55 = 5 x 5 x 5 x 5 x 5  = you tell me!

You cannot do this with two numbers which have different bases such as

53 x 42
To divide two numbers with the same base such as

105/103

Simply subtract the powers

105-3 = 102 = 10 x 10 = 100

103/105 = 103-5 = 10-2 = 0.01

 
1 milliamp  =  10-3 Amp  =  0.001 Amp

1 picoFarad  =  0.000,000,000,001 Farad  =  10-12 Farad

1 Megohm  =  1,000,000 ohms  =  106 ohms


Copyright Graham Knott 2004