## 3. Denary number position and value

When working with any number system, the *position* of the digit or symbol is important in order to be able to calculate its value.

Let's look at the denary number 123.

The number on the far right, 3, is worth 3. But the number to the left of 3 isn't worth 2. Instead, it is worth 20. Because its position is one to the left of 3, it has been multiplied by 10, so it is (10 * 2)

Now think about the number 1 in 123. Again, this isn't worth the value of 1, instead it is multiplied by 100 because it is two to the left. Its actual value is (100 * 1)

The value of the decimal number 123 is arrived at by using the following calculation:

3 + (10 * 2) + (100 * 1)

In the denary system the rightmost position is labeled "position 0".

Each time you move one position left, the value of a digit is multiplied by 10.

So a digit in position 1 is multiplied by 10. A digit in position 2 is multiplied by 100.

The following table shows the value of a "1" digit, depending on its position within a denary number

Position | 5 |
4 |
3 |
2 |
1 |
0 |

Multiplier | 10 ^{5} |
10 ^{4} |
10 ^{3} |
10 ^{2} |
10 ^{1} |
10 ^{0} |

Value | 100000 |
10000 |
1000 |
100 |
10 |
1 |

**Challenge** see if you can find out one extra fact on this topic that we haven't
already told you

Click on this link: What is place value?