Students simplify the fractions using prime factors and then they use a calculator to convert the fraction to a decimal. They then look for patterns in order to work out what the rule is for whether a fraction terminates or recurs.
The aim is to spot that once in simplified form, a fraction will recur if the denominator has any factor other than 2s or 5s.
This activity is based on one from a 1967 calculator handbook. It interleaves prime factorisation, simplifying fractions and using a calculator. It deepens students’ understanding of how fractions are simplified and leads to new knowledge about recurring decimals.