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Lesson 7 of 18

Converting terminating decimals to fractions

I can appreciate that any terminating decimal can be written as a fraction with a denominator of the form 10^n

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Lesson 7 of 18
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Converting terminating decimals to fractions

I can appreciate that any terminating decimal can be written as a fraction with a denominator of the form 10^n

Lesson details

Key learning points

  1. Place value of decimals can be represented with exponentials in the column headings.
  2. Terminating decimals have fraction equivalents.
  3. All terminating fractions can be written with exponential denominator with 10 as the base.

Keywords

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

Common misconception

The more decimal places there are, the greater the number.

Pupils can investigate this by looking at the numbers 0.23 and 0.1237 and using a common denominator or 10000.

Pupils have used prefixes of decimals in 10^n form without knowing. Ask if they can give any examples of something which is described as "micro "(10^-6). Have they ever heard of "pico" (10^-9)? The smallest recorded is "atto" (10^-18).
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
A decimal with an infinite repeating pattern of digits is called a __________ decimal.

fractional
proper
Correct answer: recurring
terminating

Q2.
Match each decimal given using dot notation to its equivalent decimal.

Correct Answer:$$0. \dot 7 \dot 8$$ ,$$0.78787878...$$

$$0.78787878...$$

Correct Answer:$$0.78 \dot 9$$ ,$$0.789999999...$$

$$0.789999999...$$

Correct Answer:$$0. \dot{7} 8 \dot {9}$$ ,$$0.789789789...$$

$$0.789789789...$$

Correct Answer:$$0. \dot 7$$ ,$$0.77777777...$$

$$0.77777777...$$

Correct Answer:$$0. 7\dot 8 \dot 9$$ ,$$0.789898989...$$

$$0.789898989...$$

Q3.
Select all the fractions which are equivalent to a recurring decimal.

Correct answer: $$\frac{5}{12}$$
$$\frac{6}{24}$$
Correct answer: $$\frac{2}{3}$$
$$\frac{9}{15}$$
Correct answer: $$\frac{2}{12}$$

Q4.
Use short division to write $$11\over15$$ as a decimal.

$$0.73$$
$$0.73333333333$$
$$0. \dot7 \dot3$$
Correct answer: $$0.7 \dot3$$

Q5.
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.

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; all decimals recur eventually.
Correct answer: No; the calculator only has a 12 digit display, the last 8 is rounded up to 9.

Q6.
Aisha writes the recurring decimal $$0.61\dot6$$ as the fraction $$\frac{\square}{60}$$. What number should she write in the square?

Correct Answer: 37

Assessment exit quiz

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6 Questions

Q1.
Terminating decimals have a number of decimal places.

Correct Answer: finite

Q2.
Write $$0.45$$ as a simplified fraction.

$$45\over100$$
Correct answer: $$9\over20$$
$$8\over20$$
$$9\over25$$

Q3.
The fraction which is halfway between 0.44 and 0.86 is $$\square \over 20$$. What number should be written in the square?

Correct Answer: 13

Q4.
Which of the following are equivalent to $$4.135$$ ?

$$835\over200$$
Correct answer: $$827\over200$$
Correct answer: $$4 \frac{27}{200}$$
$$4 \frac{135}{200}$$

Q5.
Match each decimal to a fraction with the denominator in exponential form.

Correct Answer:$$3.4$$,$$\frac{34}{10^1}$$

$$\frac{34}{10^1}$$

Correct Answer:$$0.34$$,$$\frac{34}{10^2}$$

$$\frac{34}{10^2}$$

Correct Answer:$$0.00034$$,$$\frac{34}{10^5}$$

$$\frac{34}{10^5}$$

Correct Answer:$$0.034$$,$$\frac{34}{10^3}$$

$$\frac{34}{10^3}$$

Q6.
Laura writes $$6.789 = \frac {6789}{10^ \square}$$. What number should she write in the box to make her statement true?

Correct Answer: 3, three

Lesson appears in

UnitMaths / Comparing and ordering fractions and decimals (positive and negative)

Maths

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