Place value

Explore the powerful mathematical ideas for place value and see how they grow in complexity and sophistication from Foundation through to Year 10.

The power of our number system lies in its base-10 (decimal) place value structure. Using just ten digits—0, 1, 2, 3, 4, 5, 6, 7, 8 and 9—we can represent an infinite range of numbers.

The powerful mathematical ideas in place value capture the most significant understandings that students need to develop, enabling students to work flexibly and fluently with numbers of any size. Learn how each of these powerful mathematical ideas grow in complexity and sophistication from Foundation to Year 10.

Powerful mathematical ideas in place value

10 of these is 1 of those

In base-10, each position of a digit has a value ten times the value of the position to the right. The digit $1$ in $145$ has ten times the value of the digit $1$ in $15$.

Position determines place value 

The value of a digit is determined by its position in a number. The digit $1$ represents different values in the numbers $145$ and $15$, because it is in different positions.

A number is the sum of its parts

The value represented by any number is the sum of the place values of its digits. The value of the number $145$ is the sum of the place values of its digits: $145=4 \times 100 + 4 \times 10 + 5 \times 1$.