Terminating or recurring decimal test: Class 10 practice
A fraction p/q in lowest terms has a terminating decimal exactly when q's prime factors are only 2s and 5s. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Prime factorisation
- Simplifying fractions
The idea behind terminating or recurring decimal test
A fraction p/q in lowest terms has a terminating decimal exactly when q's prime factors are only 2s and 5s. Otherwise the decimal recurs.
Step-by-step method
- Simplify the fraction fully.
- Prime factorise the denominator.
- Only 2s and 5s → terminating; anything else → recurring.
Worked example 1 (Basic)
Without dividing, does 27/10 have a terminating decimal?
- 10 = 2 × 5
- Only 2s and 5s → terminating
- Answer: Terminating
Worked example 2 (Standard)
Without dividing, does 83/150 have a terminating decimal?
- 150 = 2 × 3 × 5 × 5
- Has a prime other than 2 and 5 → recurring
- Answer: Non-terminating recurring
Worked example 3 (Challenge)
Without dividing, does 1131/1500 have a terminating decimal?
- Simplify: 1131/1500 = 377/500
- 500 = 2 × 2 × 5 × 5 × 5
- Only 2s and 5s → terminating
- Answer: Terminating
Common mistakes and misconceptions
- Testing before simplifying (e.g. 21/30 = 7/10 terminates)
- Thinking any even denominator terminates
Practice questions
- (Basic) Without dividing, does 89/200 have a terminating decimal?
- (Basic) Without dividing, does 3/4 have a terminating decimal?
- (Standard) Without dividing, does 13/8 have a terminating decimal?
- (Standard) Without dividing, does 93/40 have a terminating decimal?
- (Challenge) Without dividing, does 161/56 have a terminating decimal?
- (Challenge) Without dividing, does 10269/9800 have a terminating decimal?
Answer key with full working
- Q1: 200 = 2 × 2 × 2 × 5 × 5 → Only 2s and 5s → terminating → Answer: Terminating
- Q2: 4 = 2 × 2 → Only 2s and 5s → terminating → Answer: Terminating
- Q3: 8 = 2 × 2 × 2 → Only 2s and 5s → terminating → Answer: Terminating
- Q4: 40 = 2 × 2 × 2 × 5 → Only 2s and 5s → terminating → Answer: Terminating
- Q5: Simplify: 161/56 = 23/8 → 8 = 2 × 2 × 2 → Only 2s and 5s → terminating → Answer: Terminating
- Q6: Simplify: 10269/9800 = 1467/1400 → 1400 = 2 × 2 × 2 × 5 × 5 × 7 → Has a prime other than 2 and 5 → recurring → Answer: Non-terminating recurring
Syllabus note
This skill is listed under "Real Numbers" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is terminating or recurring decimal test in?
"Real Numbers", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.