What is the fraction of 0.36 with the 6 repeating?

2 Answers
Ben
May 9, 2018

11/30

Explanation:

Because the repeating value is a multiple of 3, I first multiplied the decimal representation by 3:

#0.3bar(666)xx3/3=1.1/3#

Since we can't have decimals in a fraction, we'll need to multiply the result above until we have all integers:

#1.1/3xx10/10=color(green)(11/30#

Since 11 is a prime number, we can't simplify the fraction any further.

Jim G.
May 9, 2018

#11/30#

Explanation:

#"we require to establish 2 equations with the repeating"#
#"number after the decimal point"#

#0.36666-=0.3bar6#

#"the bar above the 6 indicates the numeral being repeated"#

#"let "x=0.3bar6#

#rArr10x=3.bar6larrcolor(blue)"equation "(1)#

#rArr100x=36.bar6larrcolor(blue)"equation "(2)#

#"subtract "(1)" from "(2)" to eliminate repeated value"#

#(100x-10x)=(36.bar6-3.bar6)#

#rArr90x=33#

#rArrx=33/90=11/30#

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