express 0.25 (recurring) as a fraction in its simplist form?

  • -1 votes

thats the question! but REMEMBER the recurring dot is only on the 5! meaning its 0.25555555....

please help me :(

Posted Mon 28th May, 2012 @ 16:56 by amna
Edited by amna on Mon 28th May, 2012 @ 16:56

6 Answers

  • 3 votes

It's not 25/99.

Find a way to get the recurring decimals behind the decimal point (the dot) - either by multiplying it by 10, 100, or 1000 or so on. You need to find two of them.

Then, subtract the smaller number from the bigger number.

Notice the recurring number (55555555) is behind the the decimal point (below).

             x100      25.555555

             x10         2.5555555

         -

        ----------------------------------------

             x90        23

(0.555555555 take away 0.555555555 is zero so we get a whole number)

Subtract the number you multiplied them by too (100-10=90)

Then put the decimal answer over the answer you multiplied them by (if that makes sense :/).

So it becomes 23/90.

Simplify it if you can.

That's the best I can explain it. I hope it helps! :D

Also, remember to check it using your calculator - I'm assuming your paper is a calculator one as these types of questions are usually in the calculators allowed exams.

Answered Mon 28th May, 2012 @ 19:52 by FutureMedic
Edited by FutureMedic on Mon 28th May, 2012 @ 19:56
  • 1 vote

Basically what she is trying to say is that you must multiply the recurring decimal by 10 to get 2.5555 recurring and then times it by 100 to get 25.5555 recurring

You then simply take the 10 from the 100 (These came from how much you multiplied by) so then you must do the same for the answers so take the 2.55555 recurring from he 25.55555 recurring which is 23.....this is the top of the fraction

The 100 - 10 is the bottom of the fraction

The fraction would be 23/90

You then simplify this (if possible) , although 23 is a prime number and therefore cannot be simplified anymore so it stays as 23/90 which is your answer

Hope this helps :)

Luke

Answered Mon 28th May, 2012 @ 21:06 by Lukey
Edited by Lukey on Mon 28th May, 2012 @ 21:07
  • 0 votes

but how did you get there?

Answered Mon 28th May, 2012 @ 18:52 by amna
  • 0 votes

so x=0.2555555555

multiply by 100 ---->  100x=25.55555555555555

10x=2.55555555555

100x-10x=90x

25.555-2.555=23

make sense?

:D

Answered Tue 29th May, 2012 @ 19:05 by Krishna
  • -1 votes

thank you everyone this really helped! thanks lisa your explanation was perfect! and unluckily it was a non calculator paper  :(

Answered Wed 30th May, 2012 @ 19:01 by amna
  • -7 votes

25/99

Answered Mon 28th May, 2012 @ 17:14 by Aranjeet Paul