Question

Express 1.32bar+0.35bar as a fraction in simplest form

Answer 1

you can write like this 167/100 bar

Answer 2

$\huge\qquad\underline\mathfrak{Answer:}$

Let x = 1.$\bf\bar{32}$

x = 1.323232..

Since two digits are repeating therefore multiplying (2) by 100, we get

100x = 132.3232......

$\rightarrow$100x = 131+1.3232......

$\rightarrow$100x = 131+x

$\rightarrow$99x = 131

$\implies$x = $\sf\frac{131}{99}$

Also, let y = 0.$\bf\bar{35}$

y = 0.353535....

$\rightarrow$100y = 35.3535....

$\rightarrow$100y = 35+0.3535...

$\rightarrow$100y = 35+y

99y = 35

$\sf\frac{35}{99}$

0.$\sf\bar{32}+0.$$\sf\bar{35}=x+y=\frac{131}{99}+$$\sf\frac{35}{99}$

1.$\bf\bar{32}$ + 0.$\bf\bar{35}$ = $\bf\frac{166}{99}$