Recurring & Terminating Decimals: Converting Between Fractions, Decimals and Percentages

Shared by A STEM Educator★ Featured Teacher · rated 90+ in our quality review

Year 10 (KS4)BTC Style / Thinking Classrooms50 min

Learning Objective

Students will convert between fractions, terminating decimals, recurring decimals, and recurring percentages using exact algebraic methods, and identify whether a fraction produces a terminating or recurring decimal.

Lesson Overview

Students progress from identifying terminating and recurring decimals through to converting recurring decimals and recurring percentages to exact fractions using the algebraic subtraction method. Tasks change one variable at a time, building toward ceiling-level multi-digit recurring block conversions.

Materials

Vertical whiteboards or large paper
Dry-erase markers and erasers
Pencil and paper for consolidation notes
Basic calculator (to check terminating decimal conversions only)

Scaffolded Task Progression

1Task 1

Write each decimal in words and state whether it is terminating or recurring. Then write it using correct dot notation where needed.
a)

0.75

0.333...

0.1666...

0.142857142857...

2Task 2

Convert each terminating decimal to a fraction in its simplest form.
a)

0.6

0.45

0.375

0.064

3Task 3

A fraction

\frac{a}{b}

produces a terminating decimal if and only if its denominator (in simplest form) has no prime factors other than

2

and

5

. For each fraction, decide WITHOUT a calculator: does it give a terminating or recurring decimal? Explain.a)

\frac{7}{8}

\frac{5}{6}

\frac{11}{40}

\frac{7}{12}

Unlock the full lesson

See all 12 scaffolded tasks, the full answer key, warm-up, exit slip, and a print-ready version — free to start.

Create a free account

Already have an account? Sign in

Make it your own

Like this lesson but want to tweak it?

Make an editable copy and adjust the tasks, warm-up, and answer key to fit your class — no need to start from scratch.

Generate a new lesson