Write 2.445353535353... as a fraction

Question

I'm learning integrals right now and this is part of the exercises under it. Is there a trick to this? Using integrals?

Thank you very much!

Answer 1

2.44 + .0053535353 .......

2.44 + (1/100)(.53535353 .... )

.53535353... = .53 + .53/100 + .53/100^2...

= a + a r + a r^2 + a r^3.....
where
a = .53 and r = .01
sum of that infinite series
= a/(1-r)
so
.53 /(.99) = 53/99
so
we have
2.44 + (1/100)(53/99)
(1/100)( 244 + 53/99)
I think you can take it from there

Answer 2

or

let x = 2.44535353..
times 100
100x = 244.535353..
subtract them
99x = 242.09
x = 242.09/99
= 24209/9900 or 2 4409/9900

Answer 3

Do it Reiny's way (but mine is more fun)

Answer 4

And Math should be and is fun.