Question

Express the rational number `1/33` in recurring decimal form by using the recurring decimal expansion of `1/11`. Hence write `71/33` in recurring decimal form.

Answer 1

`11")"overline100("0.0909`
        99
         100
           99

`1/11` = 0.0909 ……..

= `0.bar(09)`

∴ `1/33 = 1/3 xx 1/11`

= `1/3 xx 0.0909` ……..

= 0.0303 …… 

= `0.bar(03)`

`71/33 = 2 5/33`

= `2 + 5/33`

= `2 + 5 xx 1/33`

= `2 +  5 xx 0.bar(03)`

2 + (5 × 0.030303 ……..)

2 + 0.151515 ………

`2 + 0.bar(15)`

`2. bar(15)`