The purpose of this activity is to engage students in recognising patterns in recurring decimals, and linking the size of those decimals to the division of 100 that produces them.

The background knowledge presumed for this task is outlined in the diagram below:

This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.

When 100 is divided by a whole number sometimes the answers are interesting decimals.

If you calculate 100 ÷ 11 you get this display on a calculator:

The pattern would carry on forever is the calculator screen could ever be big enough. The 1 at the end comes from rounding.

Here are some other decimal patterns that come from dividing 100 by a whole number. What number is 100 divided by to get each pattern?

What other decimal patterns can you find by dividing 100 by a whole number?

### The procedural approach (show more)

- The student uses trial and error approaches to find the missing divisor.

### The conceptual approach (show more)

- The student applies the properties of multiplication and division, particularly the inverse property to find the missing divisor and creates other patterns by systematically trialling divisors.