Question

(a) Find ten rational number between -$\frac{2}{5}$ and $\frac{1}{2}$.

(b) Insert 5 rational numbers and 2 irrational numbers between $\sqrt{2}$​ and $\sqrt{3}$​​​​.

[4 MARKS]

Answer 1

Each part: 2 Marks

(a) The LCM of denominator -5 and 2 = -10. Converting these rational numbers to equivalent rational numbers having common denominator.

$\frac{-2\times 2}{5\times 2}=\frac{-4}{10}=\frac{-4\times 2}{10\times 2}=\frac{-8}{20}$

$\frac{1\times 5}{2\times 5}=\frac{5}{10}=\frac{5\times 2}{10\times 2}=\frac{10}{20}$

Clearly -7, -6, -5.............8, 9 are integers between numerators -8 and 10 of these equivalent rational number. Thus we can take any 10 rational numbers and the numbers are $\frac{-7}{20}$, $\frac{-6}{20}$, $\frac{-5}{20}$,$\frac{-3}{20}$,$\frac{-1}{20}$, 0,$\frac{1}{20}$, $\frac{3}{20}$, $\frac{4}{20}$, $\frac{5}{20}$.


(b) $\sqrt{2}$​ = 1.414 (approx)

$\sqrt{3}$​​​​ = 1.732 (approx)

5 rational numbers between $\sqrt{2}$​ and $\sqrt{3}$​​​​ are 1.42, 1.43, 1.44, 1.45, 1.50. (there are many more)

2 irrational numbers between $\sqrt{2}$​ and $\sqrt{3}$​​​​ are $\sqrt{2}.1$ and $\sqrt{2}.9$ (there are many more)