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Number systems — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsNumber systems1 Mark
MCQ
An irrational number between $\sqrt{2}$ and $\sqrt{3}$ is:
  • A
    $\pi$ and $\frac{22}{7}$ are both rationals.
  • B
    $\pi$ and $\frac{22}{7}$ are both irrationals
  • C
    $\pi$ is rational and $\frac{22}{7}$ is irrational.
  • D
    $\pi$ is irrational and $\frac{22}{7}$ is rational.
✓

Answer

  1. $\pi$ is irrational and $\frac{22}{7}$ is rational.
    Solution:
    A number which can neither be expressed as a terminating decimal nor as a repeating decimal is called an irrational number.
    So, $\pi=3.141592...$ is irrational.
    The numbers of the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0,$ are known as rational numbers.
    So, $\frac{22}{7}$ is rational.
    Hence, the correct option is (d).

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