The value of (1.3333)(0.6666)(1.125)/(0.75)(0.8)(0.8333) is closest to

I have a question ...how do we easily find the fractional form of decimals like

1.3333 = 4/3
0.6666 = 2/3

chetan2u Bunuel

Posted from my mobile device

You have to know few conversions for that
1) 0.333.. =1/3, so if it is 2/3 or 2*1/3, multiply by 2, that is 0.333*2
2) 0.125..=1/8, so you can find 2/8 or 1/4, 3/8, 5/8 and so on
3) 0.16666...=1/6
4) 0.25=1/4, so 3/4 =0.25*3=0.75 and so on.

Change to fractions if you are comfortable with them.

\(1.3333 = 1+0.333=1+\frac{1}{3}=\frac{4}{3}\)

\(0.6666=2*0.3333=2*\frac{1}{3}=\frac{2}{3}\)

\(1.125=1+0.125=1+\frac{1}{8}=\frac{9}{8}\)

\(0.75=3*0.25=3*\frac{1}{4}=\frac{3}{4}\)

\(0.8=\frac{8}{10}\)

\(0.833=0.8+0.033=\frac{8}{10}+\frac{1}{30}=\frac{25}{30}\)

\(\frac{(1.3333)(0.6666)(1.125)}{(0.75)(0.8)(0.8333)}=\frac{\frac{4}{3}*\frac{2}{3}*\frac{9}{8}}{\frac{3}{4}*\frac{8}{10}*\frac{25}{30}}\)
\(\frac{1}{\frac{1}{2}}=2\)


But say you are not comfortable with fractions, you can always approximate the decimals as we are looking at the closest answer
Numerator = 1.3333*0.6666*1.125 = 1.3*0.7*1.1=9.1*1.1=10 ( 2 decimals brought down and one moved up to nullify the effects)
Denominator = 0.75*0.8*0.833 = 3*0.25*4*2*0.833=3*1*2*0.8=4.8~5
So \(\frac{(1.3333)(0.6666)(1.125)}{(0.75)(0.8)(0.8333)}=\frac{10}{5}=2\)

Thanks!

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