If the decimal expansion of a number terminates, what type of number is it?
Answer and explanation
Correct answer: Rational number
A terminating decimal can be expressed as a ratio of two integers by writing it over an appropriate power of 10 (for example 0.75 = 75/100 = 3/4). Therefore such numbers are rational. Option B (irrational) is incorrect because irrational numbers have non-terminating, non-repeating decimal expansions (e.g. √2). Option C (non‑real) is wrong since decimal expansions represent real numbers. Option D (natural number only) is incorrect because terminating decimals include non-integer rationals (e.g. 0.5). Exam tip: To convert a terminating decimal to a fraction, write the decimal without the point as the numerator and use 10^n as denominator where n is number of decimal places, then simplify (e.g. 0.125 = 125/1000 = 1/8).
Frequently asked questions
What is the correct answer to this question?
Rational number
Why is this the correct answer?
A terminating decimal can be expressed as a ratio of two integers by writing it over an appropriate power of 10 (for example 0.75 = 75/100 = 3/4). Therefore such numbers are rational. Option B (irrational) is incorrect because irrational numbers have non-terminating, non-repeating decimal expansions (e.g. √2). Option C (non‑real) is wrong since decimal expansions represent real numbers. Option D (natural number only) is incorrect because terminating decimals include non-integer rationals (e.g. 0.5). Exam tip: To convert a terminating decimal to a fraction, write the decimal without the point as the numerator and use 10^n as denominator where n is number of decimal places, then simplify (e.g. 0.125 = 125/1000 = 1/8).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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