Decimal Fraction

1.

Evalute : \frac{{(2.39)}^{2} - {(1.61)}^{2}}{2.39 - 1.61}

${\text{Evalute}}:\frac{{{{\left( {2.39} \right)}^2} - {{\left( {1.61} \right)}^2}}}{{2.39 - 1.61}}$

1. 2
2. 4
3. 6
4. 8

Answer:Option 1

Explanation:

Solution:

\begin{aligned} Given Expression = \\ \frac{a^{2} - b^{2}}{a - b} = \frac{(a + b) (a - b)}{(a - b)} \\ = (a + b) = (2.39 + 1.61) = 4 \end{aligned}

$\eqalign{ & {\text{Given}}\,{\text{Expression}} = \cr & \frac{{{a^2} - {b^2}}}{{a - b}} = \frac{{\left( {a + b} \right)\left( {a - b} \right)}}{{\left( {a - b} \right)}} \cr & = \left( {a + b} \right) = \left( {2.39 + 1.61} \right) = 4 \cr}$

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2.What decimal of an hour is a second ?

1. .0025
2. .0256
3. .00027
4. .000126

Answer:Option 1

Explanation:

Solution:

\begin{aligned} Required decimal = \\ \frac{1}{60 \times 60} = \frac{1}{3600} = .00027 \end{aligned}

$\eqalign{ & {\text{Required}}\,{\text{decimal}} = \cr & \frac{1}{{60 \times 60}} = \frac{1}{{3600}} = .00027 \cr}$

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3.

The value of \frac{{(0.96)}^{3} - {(0.1)}^{3}}{{(0.96)}^{2} + 0.096 + {(0.1)}^{2}} is :

${\text{The}}\,{\text{value}}\,{\text{of}}\,\frac{{{{\left( {0.96} \right)}^3} - {{\left( {0.1} \right)}^3}}}{{{{\left( {0.96} \right)}^2} + 0.096 + {{\left( {0.1} \right)}^2}}}\,{\text{is}}:$

1. 0.86
2. 0.95
3. 0.97
4. 1.06

Answer:Option 1

Explanation:

Solution:

\begin{aligned} Given expression \\ = \frac{{(0.96)}^{3} - {(0.1)}^{3}}{{(0.96)}^{2} + (0.96 \times 0.1) + {(0.1)}^{2}} \\ = (\frac{a^{3} - b^{3}}{a^{2} + a b + b^{2}}) \\ = (a - b) \\ = (0.96 - 0.1) \\ = 0.86 \end{aligned}

$\eqalign{ & {\text{Given}}\,{\text{expression}} \cr & = \frac{{{{\left( {0.96} \right)}^3} - {{\left( {0.1} \right)}^3}}}{{{{\left( {0.96} \right)}^2} + \left( {0.96 \times 0.1} \right) + {{\left( {0.1} \right)}^2}}} \cr & = \left( {\frac{{{a^3} - {b^3}}}{{{a^2} + ab + {b^2}}}} \right) \cr & = \left( {a - b} \right) \cr & = \left( {0.96 - 0.1} \right) \cr & = 0.86 \cr}$

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4.If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?

1. 0.172
2. 1.72
3. 17.2
4. 172

Answer:Option 1

Explanation:

Solution:

\begin{aligned} \frac{29.94}{1.45} = \frac{299.4}{14.5} \\ = (\frac{2994}{14.5} \times \frac{1}{10}) [Here, Substitute 172 in the place of \frac{2994}{14.5}] \\ = \frac{172}{10} \\ = 17.2 \end{aligned}

$\eqalign{ & \frac{{29.94}}{{1.45}} = \frac{{299.4}}{{14.5}} \cr & = \left( {\frac{{2994}}{{14.5}} \times \frac{1}{{10}}} \right)\,\left[ {{\text{Here,}}\,{\text{Substitute}}\,172\,{\text{in}}\,{\text{the}}\,{\text{place}}\,{\text{of}}\,\frac{{2994}}{{14.5}}} \right] \cr & = \frac{{172}}{{10}} \cr & = 17.2 \cr}$

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5.When 0.232323..... is converted into a fraction, then the result is:

1. ¹/₅
2. ²/₉
3. ²³/₉₉
4. ²³/₁₀₀

Answer:Option 1

Explanation:

Solution:

0.232323... = 0. \bar{23} = \frac{23}{99}

$0.232323... = 0.\overline {23} = \frac{{23}}{{99}}$

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6.

\frac{.009}{?} = .01

$\frac{{.009}}{?} = .01$

1. .0009
2. .09
3. .9
4. 9

Answer:Option 1

Explanation:

Solution:

\begin{aligned} Let \frac{.009}{x} = .01; \\ Then x = \frac{.009}{.01} \\ = \frac{.9}{1} \\ = .9 \end{aligned}

$\eqalign{ & {\text{Let}}\,\frac{{.009}}{x} = .01; \cr & {\text{Then}}\,x = \frac{{.009}}{{.01}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{.9}}{1} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = .9 \cr}$

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7.The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:

1. 0.02
2. 0.2
3. 0.04
4. 0.4

Answer:Option 1

Explanation:

Solution:

Given expression = (11.98)² + (0.02)² + 11.98 x x.
For the given expression to be a perfect square, we must have
11.98 x x = 2 x 11.98 x 0.02 or x = 0.04

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8.3889 + 12.952 - ? = 3854.002

1. 47.095
2. 47.752
3. 47.932
4. 47.95

Answer:Option 1

Explanation:

Solution:

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

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9.0.04 x 0.0162 is equal to:

1. 6.48 x 10^-3
2. 6.48 x 10^-4
3. 6.48 x 10^-5
4. 6.48 x 10^-6

Answer:Option 1

Explanation:

Solution:

4 x 162 = 648. Sum of decimal places = 6.
So, 0.04 x 0.0162 = 0.000648 = 6.48 x 10^-4

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10.

\begin{aligned} \frac{4.2 \times 4.2 - 1.9 \times 1.9}{2.3 \times 6.1} \\ is equal to: \end{aligned}

$\eqalign{ & \frac{{4.2 \times 4.2 - 1.9 \times 1.9}}{{2.3 \times 6.1}}\, \cr & {\text{is}}\,{\text{equal}}\,{\text{to:}} \cr}$

1. 0.5
2. 1.0
3. 20
4. 22

Answer:Option 1

Explanation:

Solution:

\begin{aligned} G i v e n E x p r e s s i o n \\ = \frac{(a^{2} - b^{2})}{(a + b) (a - b)} \\ = \frac{(a^{2} - b^{2})}{(a^{2} - b^{2})} \\ = 1 \end{aligned}

$\eqalign{ & Given\,Expression \cr & = \frac{{\left( {{a^2} - {b^2}} \right)}}{{\left( {a + b} \right)\left( {a - b} \right)}} \cr & = \frac{{\left( {{a^2} - {b^2}} \right)}}{{\left( {{a^2} - {b^2}} \right)}} \cr & = 1 \cr}$

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