Terminating decimal expansion
A fraction in lowest form has a terminating decimal expansion only when its denominator has prime factors 2 and/or 5 and no other prime factors.
In one line: Only 2 and 5 can make ten.
Practice This ConceptUnderstand it
A decimal stops when the denominator can be turned into a power of 10 by multiplying only by 2s or 5s. That is why denominators like 8, 20, 40, 125, and 200 can produce terminating decimals after simplification.
Example
Formula and rule
In lowest form, a denominator of the form 2m x 5n gives a terminating decimal.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
- 17/40 is already in lowest form.
- 2Since 40 = 23 × 5, the decimal terminates: 7/40 = 0.175.
Method you can reuse
- 1Reduce the fraction to lowest form.
- 2Factorise the denominator.
- 3Check whether only 2s and 5s are present.
- 4If yes, the decimal terminates.
Visual tip
A factor tree of the denominator after simplification is enough for a quick exam check.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
After reducing 14/35 to lowest form, does its decimal terminate?
Think first, then show answerHide answer
Common wrong answer
Saying 3/14 terminates because 14 is even is wrong; the prime factor 7 is still present.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
A fraction in lowest form has a terminating decimal expansion only when its denominator has prime factors 2 and/or 5 and no other prime factors.
- 2
Add for 2 marks
Example: 3/8 = 0.375 because 8 = 23.
- 3
Add for 3 marks
A decimal stops when the denominator can be turned into a power of 10 by multiplying only by 2s or 5s.
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