What is the Base-10 Number System

If youve ever counted from 0 to 9, then youve used base-10 without even knowing what it is. Simply put, base-10 is the way we assign place  value  to numerals. It is sometimes called the decimal system because a digits value in a number is determined by where it lies in relation to the decimal point.   The Powers of 10 In base-10, each digit of a number can have an integer value ranging from 0 to 9 (10 possibilities) depending on its position. The places or positions of the numbers are based on powers of 10. Each number position is 10 times the value to the right of it, hence the term base-10. Exceeding the number 9 in a position initiates counting in the next highest position. Numbers greater than 1 appear to the left of a decimal point and have the following place values: OnesTensHundredsThousandsTen-thousandsHundred-thousands, and so on Values that are a fraction of or less than 1 in value appear to the right of the decimal point: TenthsHundredthsThousandthsTen-thousandthsHundred-thousandths, and so on 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, such as Ï€. Leading zeros do not affect a number, although trailing zeros  may be significant  in measurements. Using Base-10 Lets look at an example of a large number and use base-10 to determine each digits place value. For instance, using the whole number 987,654.125, the position of each digit is as follows: 9 has a place value of 900,0008 has a value of 80,0007 has a value of 7,0006 has a value of 6005 has a value of 504 has a value of 41 has a value of 1/10th2 has a value of 2/100th5 has a value of 5/1000th 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 B.C. show evidence of a decimal system. This system was handed over 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 B.C. 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), counting the spaces between fingers rather than the digits. Other Numeral Systems Basic computing is based on a binary or base-2 number system in which there are only two digits: 0 and 1. Programmers and mathematicians also use the base-16 or hexadecimal system, which as you can probably guess, has 16 distinct numeral symbols. Computers also use base-10 to perform arithmetic. This is important because it allows exact computation, which is not possible using binary fractional representations.