Rational numbers

Correct answer: B. Non-terminating recurring rational number

Explanation: In 0.272727\ldots, the block 27 repeats continuously, so it is a non-terminating recurring decimal and therefore a rational number. In fact, \(0.272727\ldots=\frac{27}{99}=\frac{3}{11}\). It is not a terminating decimal and it is not an integer. Exam tip: A decimal that terminates or repeats a fixed block of digits is rational.

Correct answer: C. \(\frac{5}{8},-7\)

Explanation: \(\frac{5}{8}\) is a ratio of two integers, and \(-7\) can be written as \(\frac{-7}{1}\); therefore, both are rational numbers. \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{5}\), \(\sqrt{11}\), and \(\pi\) are irrational, while \(0.101001\ldots\) is a non-terminating, non-repeating decimal. Exam tip: A number is rational if it can be written as \(\frac{p}{q}\), where \(p,q\) are integers and \(q\ne0\).

Correct answer: C. -12

Explanation: -12 is an integer. It can be written as \(\frac{-12}{1}\), so it is also a rational number. \(\frac{3}{7}\) is rational but not an integer, while \(\sqrt{15}\) and \(\pi\) are irrational. Exam tip: To check whether an integer is rational, write it as a fraction with denominator 1.