Question

$\Huge{\color{red}{\fbox{\textsf{\textbf{Question:-}}}}}$
Explain each of the following in the form of p/q :-
(i) 0.675
(ii) $0.3 \bar2$
(iii) $0.12 \bar3$



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Answer 1

Explaination :-

(i) 0.675

→ We can write 0.675 in the form of p/q as 675/1000, because there are three digits after decimal that's why we can take the denominator to 1000.

Thus, correct answer = 675/1000

(ii) $0.3 \bar2$

→ We can write $0.3 \bar2$ as x = 0.322... [Equation 1]

Thus, we must multiply both sides by 10.

x × 10 = 0.322... × 10

10x = 3.322.. [Equation 2]

Now, subtract Equation 1 from equation 2;

10x - x = 3.322... - 0.322...

✓ 9x = 3

x = 3/9

Thus, fraction of $0.3 \bar2$ will be 3/9.

(iii) $0.12 \bar3$

→ We can write $0.12 \bar3$ as x = 0.1233... [Equation 1]

Now, multiply both sides by 10;

x × 10 = 0.1233.. × 10

10x - x = 1.233.. - 0.1233..

✓ 9x = 1.1097

x = 1.1097/9

Thus, the p/q form of $0.12 \bar3$ will be 1.1097/9.