Power of 10
A power of 10 is any of the
- )
Positive powers
In
The positive 10 power related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10[(prefix-number + 1) × 3]
Examples:
- billion = 10[(2 + 1) × 3] = 109
- octillion = 10[(8 + 1) × 3] = 1027
Name | Power | Number | SI symbol |
SI prefix
|
---|---|---|---|---|
one |
0 | 1 | ||
ten |
1 | 10 | da (D) | deca |
hundred |
2 | 100 | h (H) | hecto |
thousand |
3 | 1,000 | k (K) | kilo |
)) | 4 | 10,000 | ||
hundred thousand (lakh (India)) | 5 | 100,000 | ||
million |
6 | 1,000,000 | M | mega |
ten million (crore (India)) | 7 | 10,000,000 | ||
hundred million | 8 | 100,000,000 | ||
billion (milliard) | 9 | 1,000,000,000 | G | giga |
trillion (billion) |
12 | 1,000,000,000,000 | T | tera
|
quadrillion (billiard) |
15 | 1,000,000,000,000,000 | P | peta
|
quintillion (trillion) |
18 | 1,000,000,000,000,000,000 | E | exa
|
sextillion (trilliard) |
21 | 1,000,000,000,000,000,000,000 | Z | zetta
|
septillion (quadrillion) |
24 | 1,000,000,000,000,000,000,000,000 | Y | yotta
|
octillion (quadrilliard) |
27 | 1,000,000,000,000,000,000,000,000,000 | R | ronna
|
nonillion (quintillion) |
30 | 1,000,000,000,000,000,000,000,000,000,000 | Q | quetta
|
decillion (quintilliard) |
33 | 1,000,000,000,000,000,000,000,000,000,000,000 | ||
undecillion (sextillion) |
36 | 1,000,000,000,000,000,000,000,000,000,000,000,000 | ||
duodecillion (sextilliard) |
39 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
tredecillion (septillion) |
42 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
quattuordecillion (septilliard) |
45 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
quindecillion (octillion) |
48 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
sexdecillion (octilliard) |
51 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
septendecillion (nonillion) |
54 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
octodecillion (nonilliard) |
57 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
novemdecillion (decillion) |
60 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
vigintillion (decilliard) |
63 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
unvigintillion (undecillion) |
66 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
duovigintillion (undecilliard) |
69 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
trevigintillion (duodecillion) |
72 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
quattuorvigintillion (duodecilliard) |
75 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
quinvigintillion (tredecillion) |
78 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
sexvigintillion (tredecilliard) |
81 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
septenvigintillion (quattuordecillion) |
84 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
octovigintillion (quattuordecilliard) |
87 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
novemvigintillion (quindecillion) |
90 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
trigintillion (quindecilliard) |
93 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
googol | 100 | 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 |
||
centillion |
303 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 |
||
googolplex | googol | one then 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 zeros. |
||
googolplexian | googolplex | one then (one then 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 zeros) zeros |
Negative powers
The sequence of powers of ten can also be extended to negative powers.
Similar to the positive powers, the negative power of 10 related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10−[(prefix-number + 1) × 3]
Examples:
- billionth = 10−[(2 + 1) × 3] = 10−9
- quintillionth = 10−[(5 + 1) × 3] = 10−18
Name | Power | Number | SI symbol |
SI prefix
|
---|---|---|---|---|
one | 0 | 1 | ||
tenth | −1 | 0.1 | d | deci |
hundredth | −2 | 0.01 | c | centi |
thousandth |
−3 | 0.001 | m | milli |
ten-thousandth (Myriadth) | −4 | 0.000 1 | ||
hundred-thousandth (Lacth) | −5 | 0.000 01 | ||
millionth | −6 | 0.000 001 | μ | micro |
billionth |
−9 | 0.000 000 001 | n | nano |
trillionth |
−12 | 0.000 000 000 001 | p | pico
|
quadrillionth |
−15 | 0.000 000 000 000 001 | f | femto
|
quintillionth |
−18 | 0.000 000 000 000 000 001 | a | atto
|
sextillionth | −21 | 0.000 000 000 000 000 000 001 | z | zepto
|
septillionth | −24 | 0.000 000 000 000 000 000 000 001 | y | yocto
|
octillionth | −27 | 0.000 000 000 000 000 000 000 000 001 | r | ronto
|
nonillionth | −30 | 0.000 000 000 000 000 000 000 000 000 001 | q | quecto
|
decillionth | −33 | 0.000 000 000 000 000 000 000 000 000 000 001 | ||
undecillionth | −36 | 0.000 000 000 000 000 000 000 000 000 000 000 001 | ||
duodecillionth | −39 | 0.000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
tredecillionth | −42 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
quattuordecillionth | −45 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
quindecillionth | −48 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
sexdecillionth | −51 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
septendecillionth | −54 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
octodecillionth | −57 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
novemdecillionth | −60 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
vigintillionth | −63 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
unvigintillionth | −66 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
duovigintillionth | −69 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
trevigintillionth | −72 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
quattuorvigintillionth | −75 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
quinvigintillionth | −78 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
sexvigintillionth | −81 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
septenvigintillionth | −84 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
octovigintillionth | −87 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
novemvigintillionth | −90 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
trigintillionth | −93 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
googolth | −100 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 1 | ||
centillionth | −303 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
googolplexth | −googol | ten to the negative 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000th power | ||
googolplexianth | −googolplex | ten to the negative (ten to the 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000th power) power |
Googol and googolplex
The number googol is 10100. The term was coined by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. It was popularized in Kasner's 1940 book Mathematics and the Imagination, where it was used to compare and illustrate very large numbers. Googolplex, a much larger power of ten (10 to the googol power, or 1010100), was also introduced in that book.
Scientific notation
Scientific notation is a way of writing numbers of very large and very small sizes compactly when precision is less important.
A number written in scientific notation has a significand (sometime called a mantissa) multiplied by a power of ten.
Sometimes written in the form:
- m × 10n
Or more compactly as:
- 10n
This is generally used to denote powers of 10. Where n is positive, this indicates the number of zeros after the number, and where the n is negative, this indicates the number of decimal places before the number.
As an example:
The notation of mEn, known as
See also
- Power of two
- Power of three
- SI prefix
- Cosmic View, inspiration for the film Powers of Ten
- Exponentiation
- Philip and Phylis Morrison wrote a book called "Powers of Ten: A Book About the Relative Size of Things in the Universe and the Effect of Adding Another Zero" to accompany the video of Eames. [1]
Further reading
- Video
- Powers of Ten (1977). Nine-minute film. US Public Broadcasting Service (PBS), made by Charles and Ray Eames. "An adventure in magnitudes. Starting at a picnic by the lakeside in Chicago, this film transports the viewer to the outer edges of the universe. Every ten seconds we view the starting point from ten times farther out until our own galaxy is visible only as a speck of light among many others. Returning to Earth with breathtaking speed, we move inward - into the hand of the sleeping picnicker - with ten times more magnification every two seconds. Our journey ends inside a proton of a carbon atom within a DNA molecule in a white blood cell."
References
- ^ "Powers of 10". www.mathsteacher.com.au. Retrieved 2020-03-17.
- ^ "Powers of Ten". hesperia.gsfc.nasa.gov. Retrieved 2020-03-17.