Question

Express `1.26 + 0.bar(35)` in the form of a rational number `("in fraction form" p/q)`.

Answer 1

Let x = 1.26

⇒ x = 1.2666...

Here, one digit is not repeating after decimal place,

So, multiply both sides by 10, 

10x = 12.6666...   ...(i)

Here, one digit is repeating after decimal place, 

So, multiply both sides by 10,

100x = 126.6666...   ...(ii)

Subtracting equation (i) from equation (ii).

90x = 114

⇒ `x = 114/90`

⇒ `1.26 = 38/30`   ...(iii)

Ley `y = 0.bar(35)`

⇒ y = 0.353535...   ...(iv)

Here, two digits are repeating after decimal place,

So, multiply both sides by 100, 

100y = 35.353535...   ...(v)

Subtracting equation (iv) from equation (v),

99y = 35

⇒ `y = 35/99`

⇒ `0.35 = 11.6/33`   ...(vi)

Adding equation (iii) and equation (vi),

`1.26 + 0.bar(35) = 38/30 + 11.6/33`

= `((38 xx 33)/(30 xx 33))/((11.6 xx 30)/(33 xx 30))`

= `1254/1000.89 + 348/1000.89`

= `(1254 + 348)/1000.89`

= `1602/1000.89`

= `802/495`