How do you convert 0.47 (47 being repeated) to a fraction?
1 Answer
Explanation:
First note that we can indicate the repeating part of a decimal representation by placing a bar over the repeating pattern:
#0.47474747... = 0.bar(47)#
To find the equivalent fraction, first multiply by
#(100-1) 0.bar(47) = 47.bar(47)-0.bar(47) = 47#
Then divide both ends by
#0.bar(47) = 47/(100-1) = 47/99#
This is in simplest form, since
Why
Multiplying by
Alternative method
If you know that
#0.bar(47) = 47/99 * 0.bar(99) = 47/99 * 1 = 47/99#