Question

Match the correct decimal form to its fractional form.

• A. $\frac{7}{9}$
• B. $\frac{16}{9}$
• C. $\frac{7}{11}$

Answer 1

Case 1:
Let '$x$' be 0.636363....
In this decimal, the digits 63 gets repeated. So multilpy $x$ with 100.

$\Rightarrow$ 100$x$ = 63.636363....
= 63 + 0.636363.....
= 63 + $x$ $(\because x=\mathrm{0.636363....})$

$\Rightarrow$ 99$x$ = 63
$\Rightarrow$ $x$ = $\frac{63}{99}$
= $\frac{7}{11}$

$\therefore$ Fractional form of the decimal 0.636363....... is $\frac{7}{11}.$

Case 2:
Let '$x$' be 0.7777777....
In this decimal, the digit 7 gets repeated. So multilpy $x$ with 10.

$\Rightarrow$ 10$x$ = 7.777777....
= 7 + 0.777777.....
= 7 + $x$ $(\because x=\mathrm{0.777777....})$
$\Rightarrow$ 9$x$ = 7
$\Rightarrow$ $x$ = $\frac{7}{9}$
= $\frac{7}{9}$

$\therefore$ Fractional form of the decimal 0.777777....... is $\frac{7}{9}.$

Case 3:
Let '$x$' be 1.7777777....

In this decimal, the digit 7 gets repeated. So multilpy $x$ with 10.

$\Rightarrow$ 10$x$ = 17.777777....
= 16 + 1.777777.....
= 16 + $x$ $(\because x=\mathrm{1.777777....})$
$\Rightarrow$ 9$x$ = 16
$\Rightarrow$ $x$ = $\frac{16}{9}$
= $\frac{16}{9}$
$\therefore$ Fractional form of the decimal 1.777777....... is $\frac{16}{9}.$