Decimal
Alternatively called base-10 and denary, decimal is a numbering system comprised of the numerals 0 to 9 that was first used by the Chinese in 1350 B.C. Decimals are primarily used to express numbers that are not whole numbers (e.g., fractions), such as 0.25 or 10.43. However, numbers in a decimal system can also be expressed as integers (whole numbers) rather than non-integers (fractions) with exponents that are positive instead of negative in value. For example, 102 is 100 whereas 10-2 is 0.01.
The following sections include examples to help you better understand decimal numbers and their practical application. To proceed, you may choose one that interests you or read through them all in order.
Decimal fractions
When most people think of decimals, they're referring to a decimal fraction, a partial number whose denominator is a power of ten. Its place is determined by the number of digits to the right of the decimal point or decimal separator. For example, 2/10, 2/100, and 2/1000 are expressed in decimal as 0.2, 0.02, and 0.002. In the real world, decimal fractions are used with calculators and spreadsheets to express non-whole numbers.
Decimal fraction example:
| Ones | Tenths | Hundredths | Thousandths |
|---|---|---|---|
| 0 | 6 | 8 | 2 |
The table above illustrates a decimal fraction. As you can see, there is a "0" in the ones place, a "6" in the tenths place, "8" in hundredths, and "2" in thousandths. This number is written out as 0.682.
Breakdown of a number in decimal
Here is a breakdown of a decimal number 234.567 using base-10:
234.567=(2×102)+(3×101)+(4×100)+(5×10-1)+(6×10-2)+(7×10-3)
As you can see in the example above, each number in our figure (234.567) is separated into its base-10 equivalent. Essentially, it's 200+30+4+0.5+0.06+0.007, totaling 234.567.
Whole numbers in decimal
The decimal system accounts for whole numbers, too. That is, numbers that only have values in positions left of the decimal separator (point).
Whole number decimal example:
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 0 | 5 | 9 | 3 |
The table above shows a whole number using the base-10 system. In it, there are "5" hundreds (500), "9" tens (90), and "3" ones (3), totaling the decimal number 593.
Excel and spreadsheet decimals
In a spreadsheet program like Microsoft Excel or Google Sheets, a decimal can be added or adjusted by changing the number format. For example, the default cell format is general; changing it to number, currency, or another format would also allow you to adjust the decimal point's placement and its visibility.
Programming and storing decimals
Computers store decimal numbers as a floating-point or float data type. Computers and programming languages distinguish these from integers or whole numbers for storage efficiency, mathematical computation efficiency, and level of accuracy.
Base, Binary, Dec, Decimal alignment, Factorial, Fraction, Hexadecimal, Mantissa, Octal, Round, Whole number