A recurring decimal is one that has an infinite number of digits after the decimal point.

Converting fractions to recurring decimals

Maths

In this unit, pupils have explored the structure of fractions and their relationship with decimals and integers. This is built on in the future unit where pupils deepen their understanding of the arithmetic procedures involving fractions and integers.

In this unit, pupils will be asked to compare and order both fractions and decimals and will assess when conversion is required. Fluency in working with decimals and integers is an important skill which is developed in the prior unit.

This unit develops understanding and manipulation of fractions, including conversion between fractions to terminating and recurring decimals. Pupils then learn strategies to order fractions of increasing complexity.

Comparing and ordering fractions and decimals (positive and negative)

A decimal with an infinite repeating pattern of digits is called a {{ }} decimal.

Match each decimal given using dot notation to its equivalent decimal.

Select all the fractions which are equivalent to a recurring decimal.

Use short division to write $$8\over15$$ as a decimal.

Yes; Jacob's number has 10 digits after the decimal point so it terminates.

Yes; the last digit is 7 not 6 so it doesn't repeat. So it must terminate.

No; the calculator only has a 12 digit display, the last 6 is rounded up to 7.

Jacob uses his calculator to write $$11\over12$$ as a decimal. His calculator display shows the number $$0.9166666667$$. Jacob says, "This shows my fraction terminates." Is Jacob correct? Explain why.

Izzy writes the recurring decimal $$0.71\dot6$$ as the fraction $$\frac{\square}{60}$$. What number should she write in the square? {{ }}

Terminating decimals have a {{ }} number of digits after the decimal point.

Without using a calculator, work out the decimal value of $$\frac {13}{20}$$. {{ }}

Select all the fractions that can be written as terminating decimals.

Aisha uses her calculator to convert $$0.668$$ to a fraction. She gets an answer of $$\frac {167}{\square}$$. What number should go in the square? {{ }}

Match each fraction to its terminating decimal. You can use a calculator for this question.

Sam is correct as $$330$$ has factors of $$3$$ and $$11$$

Sam is correct as only fractions with a denominator of $$10$$ terminate

Sam is wrong as $$330$$ is a multiple of $$10$$

Sam is wrong as the fraction simplifies to $$7\over10$$ which terminates

Sam says that $$231 \over 330$$ is not equivalent to a terminating decimal. Without using a calculator, explain whether Sam is correct or not. 

This lesson will be removed by end of Summer Term 2025.

Converting fractions to recurring decimals

Lesson outcome

This lesson will be removed by end of Summer Term 2025.