Express the recurring decimal into fraction.

Question

a)0.02469999999...
b)123.76111111...
c)542.8888888...
d)789.456456456...

Answer 1

I work only on the decimal part, then add on the whole number at the end

I will use b) , then you follow my steps to do the others.

For the numerator:
write down all the digits to the end of the first repeat : 761
subract the digits that did NOT repeat:
761 - 76 = 685

For the denominator:
write down a 9 for each repeating digits.
There is only 1 digit repeating, so I will use one 9
Follow this with a 0 for each digits that is not repeating. I count two digits before the repeat, so two zeros. My denominator is 900

the repeating decimal becomes 685/900
or 137/180 in lowest terms

check with a calculator:
137/180 =.76111...

to finish off, add the original 123, so
123.76111... = 123 137/180 or 22277/180

btw, you can always check your answer by division on your calculator

Answer 2

I have worked on a) but on checking answer does not satisfied a).
my answer is 2223/90000=0.0247
Please check this.

Answer 3

Should have mentioned that
.9999....
.099999...
.00999...
etc, are special cases

e.g.
show that .99999.... = 1
.099999.... = .1
.009999... = .01
etc

1/3 = .3333...
2/3 = .6666...
add them:
3/3 = .99999...
1 = .9999...

1/30 = .03333...
2/30 = .06666..
add them:
3/30 = .0999...
1/10 = .09999....
.1 = .09999...

etc

so 0.02469999999...
= 0.0246 + 0.0000999999
= .0246 + .0001
= .0247
or 247/10000 ,

The others should have worked for you

Answer 4

OK this i understand but how will I find reaped digit when i will change the fraction into recurring decimal that reaped digit is 9,8,7,6,5 in this case.