Decimal Fraction - Aptitude MCQ Questions and Solutions with Explanations

324 × 115 × 85 = 3167100
Sum of decimal place = 3
∴ 32.4 × 11.5 × 8.5 = 3167.1

$$\eqalign{ & = \frac{{3.6 \times 0.48 \times 2.50}}{{0.12 \times 0.09 \times 0.5}} \cr & = \frac{{36 \times 48 \times 250}}{{12 \times 9 \times 5}} \cr & = 800 \cr} $$

Converting each of the given fractions in to decimal form, we get
$$\frac{5}{9}$$ = 0.55
$$\frac{7}{11}$$ = 0.63
$$\frac{8}{15}$$ = 0.533
$$\frac{11}{17}$$ = 0.647
Clearly, 0.647 > 0.63 > 0.55 > 0.533
So, $$\frac{11}{17}$$ > $$\frac{7}{11}$$ > $$\frac{5}{9}$$ > $$\frac{8}{15}$$

Given expression :
$$\eqalign{ & = 3927 + \frac{{5526}}{{12.5}} \cr & = 3927 + \frac{{55260}}{{125}} \cr} $$
= 3927 + 442.08
= 4369.08

$$\frac{4}{5}$$ = 0.8
$$\frac{7}{13}$$ = 0.53
$$\frac{1}{2}$$ = 0.5
$$\frac{2}{3}$$ = 0.66
$$\frac{3}{4}$$ = 0.75
$$\frac{5}{7}$$ = 0.714
Clearly, 0.5 does not lie between 0.53 and 0.8
∴ $$\frac{1}{2}$$ does not lie between $$\frac{4}{5}$$ and $$\frac{7}{13}$$

383 × 38 × 38 = 553052
Number of decimal place = 1
∴ 383 × 38 × 3.8 = 55305.2

Converting each of the given fractions into decimal form, we get :
$$\frac{2}{3}$$ = 0.66
$$\frac{3}{4}$$ = 0.75
$$\frac{4}{5}$$ = 0.8
$$\frac{5}{6}$$ = 0.833
Since 0.833 > 0.8 > 0.75 > 0.66
So, $$\frac{5}{6}$$ > $$\frac{4}{5}$$ > $$\frac{3}{4}$$ > $$\frac{2}{3}$$
∴ Required difference = $$\left( {\frac{5}{6} - \frac{2}{3}} \right) = \frac{1}{6}$$

$$\eqalign{ & 0.121212...... \cr & = 0.\overline {12} \cr & = \frac{{12}}{{99}} \cr & = \frac{4}{{33}} \cr} $$

Given expression :
$$\eqalign{ & \left[ {1 + \frac{1}{{1 \times 2}} + \frac{1}{{1 \times 2 \times 4}} + \frac{1}{{1 \times 2 \times 4 \times 8}} + \frac{1}{{1 \times 2 \times 4 \times 8 \times 16}}} \right] \cr & = \frac{{2 \times 4 \times 8 \times 16 + 4 \times 8 \times 16 + 8 \times 16 + 16 + 1}}{{2 \times 4 \times 8 \times 16}} \cr & = \frac{{1024 + 512 + 128 + 16 + 1}}{{1024}} \cr & = \frac{{1681}}{{1024}} \cr & = 1.6416 \cr} $$

Given expression :
$$\eqalign{ & \frac{{{{\left( {0.013} \right)}^3} + 0.000000343}}{{{{\left( {0.013} \right)}^2} - 0.000091 + 0.000049}} \cr & a = 0.013 \text{ and } b = 0.007 \cr & = \left( {\frac{{{a^3} + {b^3}}}{{{a^2} - ab + {b^2}}}} \right) \cr & = a + b \cr & = 0.013 + 0.007 \cr & = 0.020 \cr} $$