Question

what rational number has the decimal expansion .272727

Answer 1

272.727

is the decimal

Answer 2

Question :- what rational number has the decimal expansion 0.272727_____ ?

Solution :-

Let us assume that the given decimal expansion is equal to x.

→ x = 0.272727___ ----------- Eqn.(1)

Multiply both sides by 100 we get,

→ 100x = 27.2727______ Eqn.(2)

Now, subtracting Eqn.(1) from Eqn.(2) we get,

→ 100x - x = (27.2727____) - (0.272727___)

→ 99x = 27

Dividing both sides by 99 ,

→ x = (27/99)

→ x = (9 * 3) / (9 * 11)

9 will be cancel from both numerator and denominator ,

→ x = (3/11) (Ans.)

Hence, the required decimal number is (3/11).