Question

Express the following in the form of p/q , where p and q are integers and q is not equal to 0. (I) 0.5555........ (ii)0.5777.............

Answer 1

Answer:  The required fraction forms of the given decimals are

(i) $0.555...=\dfrac{5}{9}.$

(ii) $y=\dfrac{286}{495}.$

Step-by-step explanation:  We are given to express the following decimals in the form of $\dfrac{p}{q}$, 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

$10\times x=0.555...\times 10\\\\\Rightarrow 10x=5.555...\\\\\Rightarrow 10x=5+0.555...\\\\\Rightarrow 10x=5+x\\\\\Rightarrow 10x-x=5\\\\\Rightarrow 9x=5\\\\\Rightarrow x=\dfrac{5}{9}.$

So, $0.555...=\dfrac{5}{9}.$

(ii) Let 0.5777 . . . =y.

Then, we have

$100\times y=0.5777...\times 100\\\\\Rightarrow 100y=57.777...\\\\\Rightarrow 100y=57.2+0.5777...\\\\\Rightarrow 100y=57.2+y\\\\\Rightarrow 100y-y=57.2\\\\\Rightarrow 99y=57.2\\\\\Rightarrow y=\dfrac{57.2}{99}\\\\\Rightarrow y=\dfrac{572}{990}\\\\\Rightarrow y=\dfrac{286}{495}.$

So, $y=\dfrac{286}{495}.$

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

(i) $0.5555...=\dfrac{5}{9}.$

(ii) $0.5777...=\dfrac{286}{495}.$

Answer 2

Answer:

(I) 5/9              (ii)   52/90

Step-by-step explanation:

(I)    x    =  0.5555--------------------------  (i)

      10x = 5.5555

      10x = 5 + 0.555

      10x = 5 + x                [from (i)]

       9x = 5

        x = 5/9

(ii)    x      =  0.5777

       10x  =  5.777-----------------(i)

       100x = 57.777-------------------(ii)

      (subtracting (ii) from (i) )

      90x    = 52

      x         = 52/90

__________________SEE YA!____________.