C
CraftExam
high importancemedium8 min

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.

Practice This Concept

Learn the concept

Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

    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. 2

    Then show how to use it

    1. Reduce the fraction to lowest form. 2. Factorise the denominator. 3. Check whether only 2s and 5s are present. 4. If yes, the decimal terminates.

  3. 3

    Add one concrete example

    3/8 = 0.375 because 8 = 2^3.

  4. 4

    Avoid this incomplete answer

    Saying 3/14 terminates because 14 is even is wrong; the prime factor 7 is still present.

Definition

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.

Example

3/8 = 0.375 because 8 = 2^3.

Rule to remember

In lowest form, a denominator of the form 2^m x 5^n gives a terminating decimal.

Memory hook

Only 2 and 5 can make ten.

Examples and method

Worked example

7/40 is already in lowest form. Since 40 = 2^3 x 5, the decimal terminates: 7/40 = 0.175.

Method to apply

1. Reduce the fraction to lowest form. 2. Factorise the denominator. 3. Check whether only 2s and 5s are present. 4. If yes, the decimal terminates.

Diagram support

A factor tree of the denominator after simplification is enough for a quick exam check.

How CBSE asks it

Identify whether a fraction terminates, or convert a fraction into a decimal and classify it.

Avoid common mistakes

Common confusion

Students check the original denominator without first reducing the fraction to lowest form.

Common wrong answer

Saying 3/14 terminates because 14 is even is wrong; the prime factor 7 is still present.

Exam tip

Always simplify the fraction first, then inspect only the denominator's prime factors.

Quick check

After reducing 14/35 to lowest form, does its decimal terminate?

Yes, because 14/35 reduces to 2/5, and the denominator has only the prime factor 5.

Answer writing and exam use

1-mark answer

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-mark answer

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 lowest form, a denominator of the form 2^m x 5^n gives a terminating decimal. 3/8 = 0.375 because 8 = 2^3.

3-mark answer

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. In lowest form, a denominator of the form 2^m x 5^n gives a terminating decimal. 7/40 is already in lowest form. Since 40 = 2^3 x 5, the decimal terminates: 7/40 = 0.175. Identify whether a fraction terminates, or convert a fraction into a decimal and classify it. Saying 3/14 terminates because 14 is even is wrong; the prime factor 7 is still present.
MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept