Decimal Fractions – 1 : Free Aptitude Test

\(101\frac{27}{100000}= 101+\frac{27}{100000}= 101+ .00027 = 101.00027.\)

\(0.36 =\frac{36}{100}=\frac{9}{25}.\) Sum of numerator and Denominator = 9 + 25 = 34

Required decimal = \(\frac{1}{60\times60}=\frac{1}{3600}= .00027\)

Let 3889 + 12.952 –x = 3854.002.
Then, x = (3889 + 12.952) – 3854.002 = 3901.952 – 3854.002 = 47.95

Let 138.009 + 341.981 – 146.305 = 123.6 + x
Then, x = (138.009 + 341.981) – (146.305 + 123.6) = 479.99 – 269.905 = 210.085

Given Product = \(0.3\times0.25\times0.5\times0.125\times24\)
= \(\left ( \frac{3}{10}\times\frac{25}{100}\times\frac{5}{10} \times \frac{125}{1000}\times24\right ) = \frac{9}{80}= \frac{1}{8}(App.)\)

Sum of decimal places = 7
Since the last digit to the extreme right will be zero \((5\times4=20)\), so there will be 6 significant digits to the decimal point.

\(\left (\frac{0.05}{0.25} + \frac{0.25}{0.05} \right )^{3} = \left ( \frac{5}{25}+\frac{25}{5} \right )^{3}=\left ( \frac{1}{5}+5 \right )^{3}= \left (\frac{26}{5} \right )^{3}=(5.2)^{3}=140.608\)

\(\frac{0.0.396}{2.51} \frac{3.96}{251} =\left ( \frac{396}{251\times100} \right ) = \frac{1.577}{100}=0.01577 = 0.016\)

\(\frac{1}{4}+\frac{1}{4\times5}+ \frac{1}{4\times5\times6}= \frac{1}{4}\left ( 1+\frac{1}{5}+\frac{1}{30} \right )= \frac{1}{4}\left ( \frac{30+6+1}{30} \right )\frac{1}{4}\times\frac{37}{30}=\frac{37}{120}= 0.3083\)