# Decimal numeration system

The decimal numeral system, also referred to as the decimal numeral system or base-10 positional numeral system, is a system for expressing numerals such that the position of the digit indicates the power of 10 that the digit is multiplied by to determine its value. For example, the integer 10 has a 1 in the tens place and a 0 in the ones place. We can expand 10 to show what it actually means in terms of the decimal numeral system:

10 = 1 × 10^{1} + 0 × 10^{0}

Similarly, 234 can be expressed as:

234 = 2 × 10^{2} + 3 × 10^{1} + 4 × 10^{0}

The charts below show the names of the positions used in the decimal numeral system and the corresponding powers of 10 used to determine their place value. The chart labeled "Whole Numbers" corresponds to digits that are left of the decimal point of a number.

Similarly, the chart labeled "Decimal Fractions" corresponds to digits to the right of the decimal point in a number.

Both charts above are not exhaustive; the Whole Numbers chart can extend further to the left for larger values such as trillions, quadrillions, etc, while the Decimal Fractions chart can extend further to the right to trillionths, quadrillionths, etc.