Question

express 0.383838....+1.277777.....as a fraction in simplest form?

Answer 1

$\textbf{ \huge{ Hello Mate! }}$

x = 0.383838..... ___(1)

Multiply 100 from x

100x = 38.383838.... ___(2)

Subtracting (1) from (2)

99x = 38

x = 38 / 99

y = 1.277777......

Multiply 10 from y

10y = 12.77777.....

10y = 12 + 0.77777.....

[ z = 0.77777..... _____(3)

Multiply 10 from z

10z = 7.7777..... ____(4)

Subtracting (3) from (4)

9z = 7

z = 7 / 9 ]

10y = 12 + 7 / 9

10y = ( 108 + 7 ) / 9

y = 115 / 90

=> 38 / 99 + 115 / 90

L.C.M of 99 and 90 is 990

= ( 38 × 10 + 115 × 11 ) / 990

= ( 380 + 1265 ) / 990

= 1645 / 990 = 329 / 198

$\textsf{ \red{ Answer is 329 / 198 }}$

$\textbf{ Have great future ahead! }$

Have great future ahead!