# Order of magnitude

scale of numbers with a fixed ratio
(Redirected from Orders of magnitude)

An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually ten, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic distributions are common in nature and considering the order of magnitude of values sampled from such a distribution can be more intuitive. When the reference value is ten, the order of magnitude can be understood as the number of digits in the base-10 representation of the value. Similarly, if the reference value is one of certain powers of two, the magnitude can be understood as the amount of computer memory needed to store the exact integer value.

If two numbers have the same order of magnitude, they are about the same size.

But if one would compare the surface of an orange with that of the earth, one would say the surface of the earth is many orders of magnitude larger than that of the orange.

Orders of magnitude are used to make approximate comparisons. If numbers differ by one order of magnitude, x is about ten times different in quantity than y. If values differ by two orders of magnitude, they differ by a factor of about 100. Two numbers of the same order of magnitude have roughly the same scale: the larger value is less than ten times the smaller value.

## List

In words
(long scale)
In words
(short scale)
Prefix (Symbol) Decimal Power[broken anchor]
of ten
Order of
magnitude
quintillionth nonillionth quecto- (q) 0.000000000000000000000000000001 10−30 −30
quadrilliardth octillionth ronto- (r) 0.000000000000000000000000001 10−27 −27
quadrillionth septillionth yocto- (y) 0.000000000000000000000001 10−24 −24
trilliardth sextillionth zepto- (z) 0.000000000000000000001 10−21 −21
trillionth quintillionth atto- (a) 0.000000000000000001 10−18 −18
billiardth quadrillionth femto- (f) 0.000000000000001 10−15 −15
billionth trillionth pico- (p) 0.000000000001 10−12 −12
milliardth billionth nano- (n) 0.000000001 10−9 −9
millionth millionth micro- (µ) 0.000001 10−6 −6
thousandth thousandth milli- (m) 0.001 10−3 −3
hundredth hundredth centi- (c) 0.01 10−2 −2
tenth tenth deci- (d) 0.1 10−1 −1
one one uni- (no symbol) 1 100 0
ten ten deca- (da) 10 101 1
hundred hundred hecto- (h) 100 102 2
thousand thousand kilo- (k) 1000 103 3
million million mega- (M) 1000000 106 6
milliard billion giga- (G) 1000000000 109 9
billion trillion tera- (T) 1000000000000 1012 12
billiard quadrillion peta- (P) 1000000000000000 1015 15
trillion quintillion exa- (E) 1000000000000000000 1018 18
trilliard sextillion zetta- (Z) 1000000000000000000000 1021 21
quadrillion septillion yotta- (Y) 1000000000000000000000000 1024 24
quadrilliard octillion ronna- (R) 1000000000000000000000000000 1027 27
quintillion nonillion quetta- (Q) 1000000000000000000000000000000 1030 30
In words
(long scale)
In words
(short scale)
Prefix (Symbol) Decimal Power[broken anchor]
of ten
Order of
magnitude