A terminating decimal is one that has a finite number of digits after the decimal point.

Converting terminating decimals to fractions

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.

Comparing and ordering fractions and decimals (positive and negative)

Terminating decimals have a {{ }} number of decimal places. 

The fraction which is halfway between 0.44 and 0.86 is $$\square \over 20$$. What number should be written in the square? {{ }} 

Which of the following are equivalent to $$4.135$$ ?

Match each decimal to a fraction with the denominator in exponential form.

Laura writes  $$6.789 = \frac {6789}{10^ \square}$$.   What number should she write in the box to make her statement true? {{ }}

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 $$11\over15$$ as a decimal.

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

Yes; the last digit is 9 not 8 so it doesn't repeat. So it must terminate.

No; the calculator only has a 12 digit display, the last 8 is rounded up to 9.

Lucas uses his calculator to write $$7\over18$$ as a decimal. His calculator display shows the number $$0.3888888889$$. Lucas says, "This shows my fraction terminates." Is Lucas correct? Explain why.

Aisha writes the recurring decimal $$0.61\dot6$$ as the fraction $$\frac{\square}{60}$$. What number should she write in the square? {{ }}

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

Converting terminating decimals to fractions

Lesson outcome

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