Orders of Magnitude Expression and Powers

Engineering Math Resources

An order of magnitude is an exponential change of plus-or-minus 1 in the value of a quantity or unit.

N = a x 10b

Where:


N = order of magnitude of a number
a = integer a
b = order of magnitude of the number

Mathematical Power  Name 
1018 or 1,000,000,000,000,000,000  one quintillion 
1015 or 1,000,000,000,000,000  one quadrillion 
1012 or 1,000,000,000,000  one trillion 
109 or 1,000,000,000  one billion 
106 or 1,000,000  one million 
103 or 1,000  one thousand 
102 or 100  one hundred 
101 or 10  ten 
100 or 1  one 
10-1 or 0.1  one-tenth 
10-2 or 0.01  one-hundredth 
10-3 or 0.001  one-thousandth 
10-6 or 0.000 001  one-millionth 
10-9 or 0.000 000 001  one-billionth 
10-12 or 0.000 000 000 001  one-trillionth 
10-15 or 0.000 000 000 000 001  one-quadrillionth 
10-18 or 0.000 000 000 000 000 001  one-quintillionth