Definition of Base 10

How Base 10 Works in Math

A base-10 abacus can be a great math teaching tool. Getty Images / ManoAfrica

Base 10 refers to the numbering system in common use that uses decimal numbers. Base 10 is also called the decimal system or denary system.

In base 10, each digit in a position of a number can have an integer value ranging from 0 to 9 (10 possibilities). The places or positions of the numbers are based on powers of ten (e.g., hundredths, tenths, tens, hundreds, thousands). Exceeding the number 9 in a position starts counting in the next highest position.

Number greater than 1 appear to the left of a decimal point. Values that are a fraction appear to the right of the decimal point. Leading zeros do not affect a number, although trailing zeros may be significant in measurements.

Every real number may be expressed in base 10. Every rational number that has a denominator with only 2 and/or 5 as the prime factors may be written as a decimal fraction. Such a fraction has a finite decimal expansion. Irrational numbers may be expressed as unique decimal numbers in which the sequence neither recurs nor ends (e.g. pi).

Example Using Base 10

Take a number like 475, base ten refers to the position, the 5 is in the one's place, the 7 is in the ten's place and the 4 is in the hundred's place. Each number is 10 times the value to the right of it, hence the term base ten. The numbers continue indefinitely in this pattern: 100000,10000,1000,100,10,1 0.1, 0.01, 0.001, 0.0001, 0.00001

Base 10 blocks are often used in early education in math to help students grasp number. Base 10 blocks have a cube to represent one, ten cube strip to represent ten and a 100 cube block to represent 100. Base 10 also represents the powers of base ten.

Origin of Base 10

Base 10 is used in most modern civilizations and was the most common system for ancient civilizations, most likely because humans have 10 fingers.

Egyptian hieroglyphs dating back to 3000 BC show evidence of a decimal system. This system was handed to Greece, although the Greeks and Romans commonly used base 5 as well. Decimal fractions first came into use in China in the 1st century BC.

The digits in modern society aren't fingers (usually), but Arabic numerals.

Some other civilizations used different number bases. For example, the Mayans used base 20, possibly from counting both fingers and toes. The Yuki language of California uses base 8 (octal), by counting the spaces between fingers rather than the digits.

Note About Base 10 and Computers

Although computers use binary and other systems, they use the decimal system or base 10 to perform arithmetic. This is important because it allows exact computation, which is not possible using binary fractional representations.