## 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.