Question

The recurring decimal 2.777777 can be expressed as ​

Answer 1

Hey there!

Answer:

25/9

Step-by-step explanation:

Given recurring decimal:

2.77777....

Let x = 2.777777              ......(i)

Multiplying eq. (i) by 10;

10x = 27.777777      ........(ii)

Subtracting eq. (i) from (ii);

    10x = 27.777777...

-      x = 2.7777777....

=========================

    9x  = 25

     x = 25/9       ← (Answer)

Hence, 2.7777.... can be expressed as 25/9 as a fraction.

Hope It helps You!

Answer 2

shortcut:

2.77777... = (27-2)/9 = 25/9..... ans...

other examples:..

2.79999999..... = (279-27)/90 = 252/90

2.78989898989... = (2789-27)/990 = 2762/990