6
QuizMultiple Choice

Rational Numbers

Question 6 • SSCR 26 Math Essentials A

Holly says 4.131131113... is a rational number. Which of the following best describes whether Holly is correct and why??

Answer
A
Holly is correct. Repeating decimals are always rational numbers.
B
Holly is correct. The number is positive and all positive numbers are rational.
C
Holly is incorrect. The decimal does not terminate, so it cannot be a rational number.
D
Holly is incorrect. The decimal part follows a pattern but does not actually repeat.

Explanation

A rational number’s decimal expansion either terminates or eventually repeats a fixed block of digits. Here the digits appear to follow a pattern, with more 1s before each 3, but that pattern does not repeat the same block. So Holly is incorrect: the decimal part follows a pattern but does not actually repeat.

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