Question

Express the following in the form of p/q form where p and q are integers 0.276bar

Answer 1

given :- 0.276276276...

here we have to to write 0.276276276... in the form of p/q where q ≠ 0 and p and q must be coprime.

➡ let x be = 0.276276276... --------(i)

multiplying both sides by 1000 (since 3 numbers are repeating)

➡ 1000 × x = 1000 × 0.276276276...

➡ 1000x = 276.276276276... --------(ii)

subtracting equation (i) from (ii)

➡ 1000x - x = 276.276276276... - 0.276276276...

➡ 999x = 276

➡ x = 276/999

➡ x = (3 × 92)/(3 × 333)

➡ x = 92/333

hence, p/q form of 0.276276276... is 92/333.

Answer 2

$\huge\underline\textbf{Answer:-}$

$</strong><strong>\</strong><strong>tiny</strong><strong>\textbf{According to the given question (0.276276276):-}$

Here we are suing the integers property (conditions)

• 0.276276276 is in form of p/q
• q (≠) should not be equal to 0
• p and q must be form of integers

=>let the number be x = 0.276276276 --equation(1)

We need to multiplying both sides by 1000 Because Number 3 is repeating

$=>1000 × x = 1000 × 0.276276276$

=>1000x = 276.276276276--Equation(2)

From equation (1) and (2)

$=>1000x - x = 276.276276276$

$0.276276276$

$=>999x = 276$

$=>x = 276/999$

$=>x = (3 × 92)/(3 × 333)$

$=>x = 92/333$

• p/q is in the form of (0.276276276) and 92/333 or (0.276276276) and 92/333 is in the form of p/q