Question

0.437(37bar) in the form of p/q

Answer 1

Question: Represent $0.4\overline{37}$in the form of p/q where p and q are co-primes.

SOLUTION

Let it be equal to x.

$</p><p>x = 0.4\overline{37} \qquad \mathtt{(1)} \\ \\ \mathtt{Multiply \; 10 \; both \; sides} \\ \\ \Rightarrow \qquad 10x = 4.\overline{37} \qquad \mathtt{2} \\ \\ \mathtt{Subtract \; (1) \; from \; (2)} \\ \\ \Rightarrow \qquad 10x - x = 4.\overline{37} - 0.4\overline{37} \\ \\ \Rightarrow \qquad 9x = 4.33 \\ \\ \Rightarrow \qquad x = \frac{4.33}{9} \\ \\ \mathtt{Multiply \; and \; divide \; 100} \\ \\ \Rightarrow \qquad x = \frac{4.33}{9} \times \frac{100}{100} \\ \\ \Rightarrow \qquad x = \frac{433}{990}$

$\huge{\pink{Answer \; : \;} \frac{433}{990}}$