The decimal #0.85# have the right to be convert to the fraction #85/100#, by definition of a decimal. This fraction, #85/100#, however, is no in simplest form. The portion can be streamlined to #17/20#, together both the numerator (top) and denominator (bottom) that the fraction are divisible by 5.

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Therefore, your answer is #color(red)(17/20#.

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The very first step we have the right to take is to put 85 end 100 due to the fact that #.85# is the same thing as 85 hundredths (we have the right to remember this by noting that there are two decimal areas in #.85#, or the numerator, meaning that there space two zeros in the denominator), which is the same thing together #85/100#.

#.85 = 85/100#

We deserve to simplify this by dividing the numerator and also denominator by the greatest typical factor (in this case, 5).

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#85/100 -: 5/5 = 17/20#

17 is a element number, so there"s no means we can simplify this further.

#.85 = 17/20#


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Tony B
Feb 19, 2018

#17/20#


Explanation:

Another method of looking at the decimal of #0.85# is

#ubrace("count that 1"s")+ubrace(("some count")/10)+ubrace(("some count")/100)+ubrace(("some count")/1000)+...##color(white)("dd.d")darrcolor(white)("dddddddd.d")darrcolor(white)("dddddddddd")darr color(white)("dddddddd.d")darr##color(white)("dddd")0color(white)("ddddddddddd")8color(white)("ddddddddddd")5#

So #0.85# is the same as #8/10+5/100#

Multiply by 1 and also you carry out not change the value. However 1 comes in numerous forms. So create as:

#color(green)(<8/10color(red)(xx1)>+5/100)#

#color(green)(<8/10color(red)(xx10/10)>+5/100)#

#color(green)(color(white)("dd") <80/100>color(white)("dd")+5/100#

#color(green)((80+5)/100#

#color(green)(85/100)#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~But 5 will certainly divide precisely into both 85 and 100

When separating or multiply what you do the optimal of a fraction you also do come the bottom. In doing so we "simplify" to an "equivalent" fraction

#color(green)((85-:5)/(100-:5) -= 17/20#

Where the symbol #-=# method "equivalent to"


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