EXPONENTS

Exponential notation is a convenient way of expressing numbers as it is a way of abbreviating a large number.

In exponential notation the exponent (written as a small superscript number) simply indicates the number of times the number that has the exponent must be multiplied by itself.

  • If the exponent is positive then the resulting number is larger than 1.
  • If the exponent is negative, the result is obtained by dividing 1 by the number (the number is in the denominator). In this case the result is smaller than 1.

Exponential notation is commonly used to write numbers with a large number of 0’s. In this case, the base (the number that has the exponent) is 10.

So:102 is ten x ten or 100

so: 10-2 is 1/(ten x ten) or .01

 

Powers of ten

 

Number

Name

Exponential notation

Common abbreviation

1/1,000,000,000

one billionth

10-9

nano..

1/1,000,000

one millionth

10-6

micro..

1/1,000

one thousandth

10-3

milli…

1/100

one hundredth

10-2

centi…

1/10

one tenth

10-1

deci…

1

one

100 **

 

10

ten

101

deca..

100

one hundred

102

 

1,000

one thousand

103

kilo..

1,000,000

one million

106

mega..

1,000,000,000

one billion

109

giga..

** Any number raised to the 0 power is defined as = to 1.

 A convenient feature of exponents used in calculations is that during multiplication exponents are added. So, if you wish to multiply 22 x 23, the answer is 25. For 101 x 103 the answer is 104.

Similarly during division, exponents are subtracted. So 100/10 = 102/101 = 101 = 10.