Question

find the value of 7.8 bar+7.88bar+7.888bar+.........upto 80 times

Answer 1

ANSWER

all numbers are mathmaticallly same because repeating unit 8 is same as 88 or 888 and so on

means

7.8bar = 7.8 8 8 8......

7.88bar = 7.88 88 88.... and so on

now for sum this we have to first convert it into fraction form

Let N = 7.8..........(1)

multiply both sides by 10

10N = 78.8.......(2)

subtract 2 from 1

we get

9N = 71

or, N =71/9

similarly

for N = 7.88 88 88.....

multiply by 10

10N = 78.8 88 88.....

we get

again N = 71/9

so sum up to 80 times

=>71/9+71/9+71/9+...............80 times

=> 80×71

9

=> 5680/9