After simplifying (264/440), what type of decimal expansion will it have?
Answer and explanation
Correct answer: Terminating
Reduce the fraction first: the greatest common divisor of 264 and 440 is 88, so 264/440 = 3/5. For a rational number in lowest terms, the decimal terminates if and only if the denominator has no prime factors other than 2 and 5. The denominator 5 satisfies this condition, and 3/5 = 0.6, a terminating decimal. Hence option B is correct. Option A would require a remaining denominator factor such as 3 or 7; option C is the pattern associated with irrational numbers; and option D is false because the value is 0.6, not a whole number.
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What is the correct answer to this question?
Terminating
Why is this the correct answer?
Reduce the fraction first: the greatest common divisor of 264 and 440 is 88, so 264/440 = 3/5. For a rational number in lowest terms, the decimal terminates if and only if the denominator has no prime factors other than 2 and 5. The denominator 5 satisfies this condition, and 3/5 = 0.6, a terminating decimal. Hence option B is correct. Option A would require a remaining denominator factor such as 3 or 7; option C is the pattern associated with irrational numbers; and option D is false because the value is 0.6, not a whole number.
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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