Powers of 10
Encyclopedia
In mathematics
, a power of ten is any of the integer
powers
of the number ten
; in other words, ten multiplied
by itself a certain number of times. By definition, the number one is a power (the zeroth power) of ten. The first few powers of ten are:
In decimal
notation the nth power of ten is written as '1' followed by n zeroes. It can also be written as 10n or as 1En in E notation. See order of magnitude
and orders of magnitude (numbers)
for named powers of ten.
The sequence of powers of ten can also be extended to negative powers:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a power of ten is any of the integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
powers
Exponentiation
Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...
of the number ten
10 (number)
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
; in other words, ten multiplied
Multiplication
Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....
by itself a certain number of times. By definition, the number one is a power (the zeroth power) of ten. The first few powers of ten are:
- 1, 1010 (number)10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
, 100100 (number)100 is the natural number following 99 and preceding 101.-In mathematics:One hundred is the square of 10...
, 1000, 1000010000 (number)10000 is the natural number following 9999 and preceding 10001.-Name:Many languages have a specific word for this number: In English it is myriad, in Ancient Greek , in Aramaic , in Hebrew רבבה , in Chinese , in Japanese [man], in Korean [man], and in Thai หมื่น [meun]...
, 100000100000 (number)One hundred thousand is the natural number following 99999 and preceding 100001. In scientific notation, it is written as 105.In South Asia, one hundred thousand is called a lakh...
, 1000000MillionOne million or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione , from mille, "thousand", plus the augmentative suffix -one.In scientific notation, it is written as or just 106...
...
| Name | Power | Number | SI prefix SI prefix The International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol... |
|---|---|---|---|
| One | 0 | 1 | |
| Ten | 1 | 10 | deca |
| Hundred | 2 | 100 | hecto |
| Thousand | 3 | 1,000 | kilo |
| Million | 6 | 1,000,000 | mega |
| Billion (Milliard) | 9 | 1,000,000,000 | giga |
| Trillion (Billion) | 12 | 1,000,000,000,000 | tera |
| Quadrillion | 15 | 1,000,000,000,000,000 | |
| Quintillion | 18 | 1,000,000,000,000,000,000 |
In decimal
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
notation the nth power of ten is written as '1' followed by n zeroes. It can also be written as 10n or as 1En in E notation. See order of magnitude
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
and orders of magnitude (numbers)
Orders of magnitude (numbers)
This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the short scale, which is used in English speaking countries, as well as a name in the long scale, which is used in some of the...
for named powers of ten.
The sequence of powers of ten can also be extended to negative powers:
| Name | Power | Number | SI prefix SI prefix The International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol... |
|---|---|---|---|
| Tenth | −1 | 0.1 | deci |
| Hundredth | −2 | 0.01 | centi |
| Thousandth | −3 | 0.001 | milli |
| Millionth | −6 | 0.000 001 | micro |
| Billionth | −9 | 0.000 000 001 | nano |