Q. Which of the following are rational numbers?Multi-select Choices:(A) 21(B) −10(C) 1.777...(D) −7
Definition of Rational Number: A rational number is a number that can be expressed as the quotient or fractionqp of two integers, where p is the numerator, q is the denominator, and q=0. Let's evaluate each option to determine if it is a rational number.
Option (A) Evaluation: Option (A) is 21. This is a fraction where the numerator is 1 and the denominator is 2. Since both 1 and 2 are integers and the denominator is not zero, 21 is a rational number.
Option (B) Evaluation: Option (B) is −10. This can be expressed as a fraction −10/1, where the numerator is −10 and the denominator is 1. Since both −10 and 1 are integers and the denominator is not zero, −10 is a rational number.
Option (C) Evaluation: Option (C) is 1.777… The ellipsis (…) indicates that the number is repeating indefinitely. If 1.777… is a repeating decimal, then it can be expressed as a fraction, which would make it a rational number. However, we need to confirm if the decimal is indeed repeating. If it is not repeating and is instead a non-repeating, non-terminating decimal, then it would not be a rational number. Since the problem does not specify that 1.777… is repeating, we cannot assume it is rational without further information.
Option (D) Evaluation: Option (D) is −7. This can be expressed as a fraction −17, where the numerator is −7 and the denominator is 1. Since both −7 and 1 are integers and the denominator is not zero, −7 is a rational number.
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