Which number can be written in the form \(\frac{p}{q}\), where (p) and (q) are integers and (q\ne0)?
Answer and explanation
Correct answer: \(0.\overline{37}\)
\(0.\overline{37}=0.373737\ldots\) is a recurring decimal, so it is a rational number. It can be written as \(\frac{37}{99}\), where both numerator and denominator are integers and the denominator is non-zero. In contrast, \(\sqrt{11}\) and \(\sqrt{13}\) are square roots of non-perfect squares and are irrational; \(\pi\) is also irrational. Exam tip: every terminating or recurring decimal is rational.
Frequently asked questions
What is the correct answer to this question?
\(0.\overline{37}\)
Why is this the correct answer?
\(0.\overline{37}=0.373737\ldots\) is a recurring decimal, so it is a rational number. It can be written as \(\frac{37}{99}\), where both numerator and denominator are integers and the denominator is non-zero. In contrast, \(\sqrt{11}\) and \(\sqrt{13}\) are square roots of non-perfect squares and are irrational; \(\pi\) is also irrational. Exam tip: every terminating or recurring decimal is rational.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Rational numbers.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
