Translating between repeating decimals and fractions

This lesson develops the concept of translating between decimal and fraction notation, particularly when decimals are repeating. This is achieved by

• Creating and solving simple liner equations to find the fractional equivalent of a repeating decimal
• Understanding the effect of multiplying a decimal by a power of 10

The initial activity gives a method for converting a repeating decimal to a fraction by multiplying the decimal by 10 to the power of the cycle of the repeating digits.

The main activity is to match together cards that show:

• Repeating decimals
• An equation to convert the decimal to a fraction
• Fractions

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.