MA wrote:

anirban16 wrote:

Express the repeating decimal .1405405405405405.... as a fraction in lowest terms.

=26/185

Alright guys, here is the process:

suppose x=.1405405405405405, which is actually is not a repeating decimal. lets make it as repeting decimal by multiplying 10 (because with this multiplication 1 comes before the decimal and remaining decimal will be the repeating decimal) as under:

(i) 10x=1.405405405405

(ii) multiply this eq by 10^3 (because there are 3 repeating numbers: 4, 0, and 5) => 1,000(10x)=1405.405405405405405405405405405405

(iii) now, substract 10x from both side (because we are eliminating the decimal)

9,990x=1405.405405405-1.405405405

x=1404/9990=26/185

i believe, this method can be applied in any fractions. for example

x=0.2222222222222222222222222222222

(i) x=0.222222222222222

(ii) 10x= 2.2222222222222222

(iii) 9x=2

x =2/9