Question #0426c

1 Answer
Jan 5, 2017

Answer:

#0.8bar(7) = 79/90#

Explanation:

Let #x = 0.8bar(7)#

#=> 10x = 8.bar(7)#

#=> 10x - x = 8.bar(7) - 0.8bar(7)#

#=> 9x = 8.7 - 0.8#

#=> 9x = 7.9#

#=> 9x = 79/10#

#=> x = 79/10*1/9#

#:. x = 79/90#

This technique of multiplying by #10# (or a power of #10#) and subtracting can be used to find the fractional representation of any number with infinitely repeating decimal digits. This answer contains a detailed explanation.