How do you convert 29.2987 (987 being repeated) to a fraction?

Question

Nathan Axel · Accepted Answer

#29.2bar(987) = 19513/666#

Multiply by #10(1000-1) = 10000-10# to get an integer: #(10000-10)*29.2bar(987)# #=292987.bar(987) - 292.bar(987)# #=292695# The factor #10# is to shift the original number so that the repeating portion starts just after the decimal point. The factor #(1000-1)# is to further shift the number #3# places and subtract the original to cancel out the pattern that repeats every #3# digits. Then dividing both ends by #(10000-10)# we find: #29.2bar(987) = 292695/(10000-10) = 292695/9990 = (color(red)(cancel(color(black)(15)))*19513) / (color(red)(cancel(color(black)(15)))*666) = 19513/666#

Eva Abramson · Answer

undefined To convert 29.2987 (987 being repeated) to a fraction, you can use the following steps:

1. Let x = 29.2987 (987 being repeated).
2. Multiply x by 1000 to move the repeating decimal places to the right: 1000x = 29298.7987 (987 being repeated).
3. Subtract x from 1000x to eliminate the repeating decimal: 1000x - x = 29298.7987 - 29.2987.
4. Simplify the equation: 999x = 29269.5.
5. Divide both sides by 999: x = 29269.5 / 999.
6. Simplify the fraction if possible.

So, 29.2987 (987 being repeated) as a fraction is 29269.5 / 999.