What type of decimal expansion will 61/90 have?
Answer and explanation
Correct answer: Non-terminating recurring
The fraction 61/90 is already in lowest terms because 61 is prime and does not divide 90. Factor the denominator: 90 = 2 × 3² × 5. A reduced rational fraction has a terminating decimal only when its denominator contains no primes other than 2 and 5. Since 3 remains as a factor, the decimal cannot terminate; because every rational number has either a terminating or an eventually repeating decimal, it must be non-terminating recurring. Thus option B is correct. Option A ignores the factor 3, option C describes an irrational decimal, and option D is not a valid classification for this fraction.
Frequently asked questions
What is the correct answer to this question?
Non-terminating recurring
Why is this the correct answer?
The fraction 61/90 is already in lowest terms because 61 is prime and does not divide 90. Factor the denominator: 90 = 2 × 3² × 5. A reduced rational fraction has a terminating decimal only when its denominator contains no primes other than 2 and 5. Since 3 remains as a factor, the decimal cannot terminate; because every rational number has either a terminating or an eventually repeating decimal, it must be non-terminating recurring. Thus option B is correct. Option A ignores the factor 3, option C describes an irrational decimal, and option D is not a valid classification for this fraction.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
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