The decimal numeral system (decimal system), or base-10 number system, represents numeric values using ten symbols, usually 0 to 9, providing the following symbols in ascending order: 0 1 2 3 4 5 6 7 8 9
Digits in the decimal system are organised into columns, for example the columns for 123 are:
| hundreds | tens | ones | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 |
| 1 | * | 100 | = | 100 |
| 2 | * | 10 | = | 20 |
| 3 | * | 1 | = | 3 |
123 |
Each of the columns contains a digit multiplied by a power of ten. The digit in the hundreds column is multiplied by ten to the power of two, which is one multiplied by ten two times, i.e. 1 * 10 * 10 = 100. Ten to the power of two is displayed as 102. Using this notation, the columns for 123 are:
| 102 | 101 | 100 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 |
| 1 | * | 102 | = | 1 | * | ( 1 * 10 * 10 ) | = | 1 | * | 100 | = | 100 |
| 2 | * | 101 | = | 2 | * | ( 1 * 10 ) | = | 2 | * | 10 | = | 20 |
| 3 | * | 100 | = | 3 | * | ( 1 ) | = | 3 | * | 1 | = | 3 |
|
123
|
The number 123 is ( 1 * 102 ) + ( 2 * 101 ) + ( 3 * 100 ).
As the decimal system uses digits 0 to 9 to represent numbers, to put a larger number than 9 in column 10n it is neccesary to multiply 10 * 10n, which gives 10n+1 and carry a column to the left. For example, putting 12 in the 100 column is impossible, so a 1 is put in the 101 column and a 2 in the 100 column, thus using two columns. Twelve is 12 * 100 = 100( 10 + 2 ) = ( 1 * 101 ) + ( 2 * 100 ).
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