Learn – Arithmetic – Rational numbers

Lesson Notes
Problem set 1
Problem set 2
Problem set 3


Lesson Notes

  • A rational number is a number of the form \frac{p}{q} where p and q are integers, and q\ne 0.


Problem set 1

Which of the following are rational numbers?

  1. \frac{-7.9235}{-4.2}
  2. \sqrt{3}
  3. \sqrt{9}+\sqrt{4}
  4. 1.31792792792792\cdots
  5. 1.3179799799979999\cdots


Problem set 2

Express the following rational numbers as fractions – that is, in the form \frac{p}{q} where p and q are integers.

  1. -27.52739
  2. -\frac{1.01}{99999}
  3. -\frac{0.02}{40}
  4. 1.\overline{3}
  5. 1.71\overline{32}


Problem set 3

Which of the following are rational numbers? For each rational number, express the number in the form \frac{p}{q}, where p and q are integers.

  1. -\sqrt{\frac{24}{6}}
  2. \frac{\sqrt{36}}{\sqrt{25}}
  3. \sqrt{2^2}
  4. \left(\sqrt{2}\right)^2
  5. 2\times 10^{-5}
  6. \sqrt{0.0001}