Which statement is correct if a decimal is terminating?
Answer and explanation
Correct answer: It is a rational number
A terminating decimal can be written as an integer divided by a power of 10, so after reducing it can be expressed as \\(\frac{p}{q}\\). For example, \\(0.125=125/1000=1/8\\). Therefore a terminating decimal is rational and (since all rationals are real) also a real number. Option B is wrong because irrational numbers have nonterminating, nonrepeating decimals. Option C is incorrect because decimals represent real numbers. Option D is wrong since terminating decimals need not be natural numbers (only some, like 1.0, are). Exam tip: convert the decimal to a fraction or check if its decimal expansion terminates or repeats — terminating or repeating implies rationality.
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What is the correct answer to this question?
It is a rational number
Why is this the correct answer?
A terminating decimal can be written as an integer divided by a power of 10, so after reducing it can be expressed as \\(\frac{p}{q}\\). For example, \\(0.125=125/1000=1/8\\). Therefore a terminating decimal is rational and (since all rationals are real) also a real number. Option B is wrong because irrational numbers have nonterminating, nonrepeating decimals. Option C is incorrect because decimals represent real numbers. Option D is wrong since terminating decimals need not be natural numbers (only some, like 1.0, are). Exam tip: convert the decimal to a fraction or check if its decimal expansion terminates or repeats — terminating or repeating implies rationality.
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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