Denary

Denary is the number system you use every day — prices in a shop, scores in a game, the number of a bus. It is called base 10 because it is built from exactly ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Having only ten digits is what makes the columns behave the way they do. Once you reach 9 you have run out of digits, so you start a fresh column on the left and begin again at 0. That is why every column is worth ten times the column to its right.

Place value is the value a digit gains from the column it sits in, so the same digit can mean very different amounts in different columns.

Here is a worked example. In the number 694, the 6 is in the hundreds column, so it stands for 6 × 100 = 600. The 9 is in the tens column, so it stands for 9 × 10 = 90. The 4 is in the ones column, so it stands for 4 × 1 = 4. Adding the columns gives 600 + 90 + 4 = 694, which is the number you started with.

The right-hand column is always the ones column, so a digit sitting there is worth exactly its face value. A zero still matters, though: 704 and 74 are different numbers, because the 0 in 704 holds the tens column open and keeps the 7 in the hundreds.