Express 3.2304 (dot above 2 and 4) as a fraction

Question

Please show working out too

Answer 1

I don't know which method you use, but here is one of the more common ways ....

let x = 3.230423042304...

multiply by 10000 , (there are 4 digits in the repeating loop, so a zero for each repeating digit)

10000x = 32304.23042304..
subtract them
9999x = 32301
x = 32301/9999 = 3589/1111

shortcut:

look only at the decimal.
for the numerator write down all the digits to the end of the repeating loop --- 2304
subtract all those digits that don't repeat -- none to subtract
for the denominator:
write down a 9 for each of the repeating digits -- 9999
add a zero for each non-repeating digit -- no zeros to add

so 3.230423042304... = 3 + 2304/9999 = 32301/9999 = 3589/1111

Answer 2

given that 6/11= 0.54 write the recurring 0.554 as a fraction 5/33 = 0.15