What is #0.375# as a fraction ?

Here's a general method for converting terminating decimal expansions into fractions...

• If the last non-zero decimal digit is #2,4,6# or #8#, then write down #color(red)(5)# and multiply by it.

• If the last non-zero decimal digit is #5#, then write down #color(red)(2)# and multiply by it.

• If the last non-zero digit is something else (i.e. #1#, #3#, #7# or #9#) then write down #color(red)(10)# and multiply by it.

• Repeat until you end up with an integer.

• Multiply all the #color(red)(5)#'S, #color(red)(2)#'s or #color(red)(10)#'s you found together to form the denominator of your fraction and use the integer you ended up with as the numerator.

Quindi nel nostro esempio:

• #0.375# termina con #5#, so write down #color(red)(2)# and double #0.375# ottenere #0.75#

• #0.75# termina con #5#, so write down #color(red)(2)# and double #0.75# ottenere #1.5#

• #1.5# termina con #5#, so write down #color(red)(2)# and double #1.5# ottenere #3#.

• Having reached an integer #3#, we find the required fraction is:

  #3/(color(red)(2) * color(red)(2) * color(red)(2)) = 3/8#