Question

express the following in form of p by q where p and q are integers and q is not equal to zero


1. 0.555
2. 12.3434​

Answer 1

Answer: The required fraction forms of the given decimals are

i) 0.555... =

.

ii) y =

.

Step-by-step-explanation: We are given to express the following decimals in the form of

.

, where p and q are integers and q is not equal to 0.

i)0.5555........

ii)0.5777

The conversions of the given decimals to fraction forms are as follows :

(i) let 0.5555... = x.

then, we have

x=0.555...

10x=5.555...

10x=5+0.555...

10x=5+x 10x-

x=5

9x=5 x={5}

{9}.

So, 0.555...={5}{9}

(ii) let 0.5777...=y.

then, we have

y=0.5777...

100

100y=57.777...

100y=57.2+0.5777...

100y=57.2+y

y=57.2

99y=57.2

y={57.2}{99}

y={572}{99}

y={286}

{495}

So, y={286}{495}

Thus, we the required fraction forms of the given decimals are

(i)0.5555...={5}{9}

(ii)0.5777...={286}{495}