# Composing numbers

The decimal system is used world-wide and students will need to understand that numbers in differing positions have different values, and that a whole number is composed of those values.

For example, the number 357 is made up (or composed) of three hundreds, five tens and seven ones:

3 × 100 + 5 × 10 + 7 × 1 = 300 + 50 + 7 = 357

The number 35.7 is made up (or composed) of three tens, five ones and seven tenths:

3 × 10 + 5 × 1 + 7 × 0.1 = 30 + 5 + 0.7 = 35.7

It is important not to forget to use examples of numbers containing a zero so that the students understand that sometimes there are no tens and/or no units.

For example, the number 907 is made up (or composed) of 9 hundreds and 7 units. Note that there are no ‘tens’ recorded, which might confuse the students with the number 97. In fact, the number 907 is composed of:

9 × 100 + 0 × 10 + 7 × 1 = 900 + 0 + 7 = 907

The students need to clearly understand that numbers are made up in this way before they start to add or subtract them. One way to be sure that they do understand is to check that they are able to articulate the way that numbers are composed. Often this stage is overlooked. Once students have a secure understanding of how numbers are composed then decomposition makes much more sense!

1 Composition and decomposition