Decimal Fractions Questions and Answers

Answer: D

\(\dfrac {5}{8} = .625\)
\(\dfrac {7}{12} = .5833\)
\(\dfrac {3}{4} = .75\)
\(\dfrac {13}{16} = .8125\)
So order will be
\(\dfrac {7}{12} < \dfrac {5}{8} < \dfrac {3}{4}< \dfrac {13}{16}\)

Answer: C

\(\dfrac {29.94}{1.45}\\~\\= \dfrac {299.4}{14.5} \\~\\ =\left ( \dfrac {2994}{14.5} \times \dfrac {1}{10} \right )\\~\\=\dfrac {172}{10} \left [ \because \dfrac {2994}{14.5} = 172 \right ]\\~\\= 17.2\)

Answer: D

\(4.\overline{86} = \left(4 + \dfrac{86}{99}\right)\)
\(3.\overline{71} = \left(3 + \dfrac{71}{99}\right)\)
Hence,
\(4.\overline{86} - 3.\overline{71} \\~\\= \left(4 + \dfrac{86}{99}\right) - \left(3 + \dfrac{71}{99}\right)\\~\\ = \left( 1 + \dfrac{15}{99}\right)\\~\\ = 1.\overline{15}\)

Answer: D

The unknown is subtracted, so move it across and move the right-hand side back:

\[ 3889 + 12.952 - x = 3854.002 \]

\[ x = 3889 + 12.952 - 3854.002 \]

\[ 3889.000 + 12.952 = 3901.952 \]

\[ 3901.952 - 3854.002 = 47.950 \]

Written without the trailing zero this is \( 47.95 \). The distractors sit within a few hundredths of it, so the decimal columns must be lined up carefully.

Answer: C

\(\dfrac 23=0.66\\ \dfrac 34=0.75\\ \dfrac 45=0.8\\ \dfrac 56=0.833\)

So biggest is \(\dfrac 56\) and smallest is \(\dfrac 23\)
Their difference is \(\dfrac 56 - \dfrac 23 = \dfrac 16\)

Answer: A

\((a + b)^2 = a^2 + 2ab + b^2\)
\(12.86 \times 12.86 + 12.86 \times p + 0.14 \times 0.14\)
\(= (12.86)^2 + 12.86 \times p + (0.14)^2\)
This can be written as,
\((12.86 + 0.14)^2 = 13^2\)
If, \(12.86 \times p = 2 \times 12.86 \times 0.14\)
i.e., if \(p = 2 \times 0.14 = 0.28\)

Answer: B

Suppose commodity X will cost 40 paise more than Y after z years.
Then,
\((4.20 + 0.40z) - (6.30 + 0.15z) = 0.40\\ \Rightarrow 0.25z = 0.40 + 2.10\\ \Rightarrow z= \dfrac {2.50}{0.25} = \dfrac {250}{25} = 10\)

X will cost 40 paise more than Y 10 years after 2001 i.e., 2011

Answer: C

Shifting the decimal point moves both numbers by a known power of ten, so the answer follows from the one given without redoing the division.

\[ \frac{29.94}{1.45} = \frac{2994 \div 100}{14.5 \div 10} = \frac{2994}{14.5} \times \frac{10}{100} = 172 \times \frac{1}{10} = 17.2 \]

The numerator shrank by a factor of 100 and the denominator by only 10, so the quotient shrinks by the ratio of those, a factor of 10.

Answer: C

The expression is set up to be the square of a sum. Comparing with

\[ (a+b)^{2} = a^{2} + 2ab + b^{2} \]

the outer terms give \( a = 11.98 \) and \( b = 0.02 \), so the middle term must be

\[ 2ab = 2(11.98)(0.02) = 0.4792 \]

The middle term as written is \( 11.98x \), so

\[ 11.98x = 0.4792 \quad\Longrightarrow\quad x = 2(0.02) = 0.04 \]

The square is then \( (11.98 + 0.02)^{2} = 12^{2} = 144 \). Notice the shortcut: \( x \) is simply twice the smaller number, so the decimals never need multiplying out.

Answer: D

Line the decimal points up and add each column.

(i)

\[ 6202.5 + 620.25 + 62.025 + 6.2025 + 0.62025 = 6891.59775 \]

(ii)

\[ 5.064 + 3.98 + 0.7036 + 7.6 + 0.3 + 2 = 19.6476 \]

The first sum has five decimal places because its longest term does, and the second has four for the same reason. Checking the number of decimal places is often enough to eliminate wrong options without adding at all.