Decimals MCQ Quiz - Objective Question with Answer for Decimals - Download Free PDF

Given:

The value of \(\frac{{{{\left( {0.96} \right)}^3} - {{\left( {0.1} \right)}^3}}}{{{{\left( {0.96} \right)}^2} + 0.096 + {{\left( {0.1} \right)}^2}}}{\rm{ }}\)

Formula Used:

\(\frac{a^3 - b^3}{a^2 + ab + b^2} = a - b\)

Calculation:

Here, a = 0.96 and b = 0.1 .

Using the formula:

\(\frac{{(0.96)^3 - (0.1)^3}}{{(0.96)^2 + (0.96 \times 0.1) + (0.1)^2}}\)

⇒ \(\frac{{(0.96)^3 - (0.1)^3}}{{(0.96)^2 + 0.096 + (0.1)^2}}\)

⇒ 0.96 - 0.1

⇒ 0.86

The correct answer is option 3.

Givan:

( 7.03 )³ - 0.027 / ( 7.03 )² +2.109 + ( 0.3 )²

Formula used:

( a³ - b³ ) = (a - b ) ( a² + ab + b²) 

Calculation:

According to the question

⇒ ( 7.03 )³ - ( 0.3 )³ /( 7.03 )² + 2.109 + ( 0.3 )²

According to the formula 

⇒ ( 7.03 - 0.3 ) { ( 7.03 )² + 7.03 × 0.3 + ( 0.3 )² } / ( 7.03 )² + 2.109 +( 0.3 )²

⇒ (7.03 - 0.3 ) = 6.73

∴ ( 7.03)³ - 0.027 / ( 7.03 )² + 2.109 + ( 0.3 )²  is 6.73.

Given:

6.3 × 6.3 + 2 × 6.3 × 3.7 + 3.7 × 3.7

Formula used:

(a + b)² = a² + 2ab + b²

Calculation:

6.3 × 6.3 + 2 × 6.3 × 3.7 + 3.7 × 3.7

⇒ (6.3 + 3.7)²

⇒ 10²

⇒ 100

∴ The correct answer is option (2).

Given:

The decimal expansion of (1/2) + (1/3).

Formula Used:

To add fractions: (a/b) + (c/d) = (ad + bc) / (bd).

Calculation:

(1/2) + (1/3)

⇒ (1×3 + 1×2) / (2×3)

⇒ (3 + 2) / 6

⇒ 5 / 6

Decimal expansion of 5 / 6:

5 ÷ 6 = 0.8333…

⇒ Decimal expansion of (1/2) + (1/3) = 0.83̅.

Therefore, the correct option is 2.

Given:

0.1 × 0.01 = ?

Calculation:

0.1 × 0.01

⇒ 0.1 × 0.01 = 0.001

∴ The correct answer is option (1).

\(\sqrt {{{\left( {0.65} \right)}^2} - {{\left( {0.16} \right)}^2}} \)

Since,

a2 - b2 = (a - b) ( a + b)

\(\begin{array}{l} \Rightarrow \sqrt {\left( {0.65 + 0.16} \right)\left( {0.65 - 0.16} \right)} \\ \Rightarrow \sqrt {\left( {0.81} \right)\left( {0.49} \right)} \\ \Rightarrow \sqrt {\left( {0.9} \right)\left( {0.9} \right) \times \left( {0.7} \right)\left( {0.7} \right)} \end{array}\)

⇒ 0.9 × 0.7 = 0.63

Given expression,

(81.84 + 118.16) ÷ 5³ = 1.2 × 2 + ?

⇒ 200 ÷ 5³ = 1.2 × 2 + ?

⇒ 200 ÷ 125 = 1.2 × 2 +?

⇒ 1.6 = 2.4 + ?

⇒ ? = -0.8

Concept used:

Given expression is,

⇒ (?)³ × 10 = 13230 ÷ (9.261 ÷ 7)

⇒ (?)³ × 10 = 13230 ÷ (1.323)

⇒ (?)³ × 10 = 10000

⇒ (?)³ = 1000

⇒ (?)³ = (10)³

Mistake Points

In this type of question, in the numerator, there are 6.75 and 4.25, while in the denominator there is 67.5, and 42.5 is present in multiplication.

From the denominator, we can write 67.5 × 67.5 as 6.75 × 10 × 6.75 × 10 = 100 × (6.75), and similarly for other terms.

Therefore we take 100 as common from the denominator.

Identity used:

a³ - b³ = (a - b) (a² + b² + ab)

Calculation:

\(\Rightarrow \text{ }\!\!~\!\!\text{ }\frac{6.75~\times ~6.75~\times ~6.75-4.25~\times ~4.25~\times ~4.25}{67.5~\times ~67.5~+~42.5~\times ~42.5~+~67.5~\times ~42.5}\)

\( \Rightarrow {\rm{}}\frac{{\left[ {\left( {6.75{\rm{\;}}-{\rm{\;}}4.25} \right)\left( {6.75{\rm{\;}} \times {\rm{\;}}6.75{\rm{\;}} + {\rm{\;}}4.25{\rm{\;}} \times {\rm{\;}}4.25{\rm{\;}} + {\rm{\;}}6.75{\rm{\;}} \times {\rm{\;}}4.25} \right)} \right]}}{{[100{\rm{\;}} \times {\rm{\;}}\left( {6.75{\rm{\;}} \times {\rm{\;}}6.75{\rm{\;}} + {\rm{\;}}4.25{\rm{\;}} \times {\rm{\;}}4.25{\rm{\;}} + {\rm{\;}}6.75{\rm{\;}} \times {\rm{\;}}4.25} \right)}}\)

⇒ ? = 2.5/100

⇒ ? = 0.025

∴ ? = 0.025

1132.757 – 2315.996 – 1753.829 + 2 × 2846.639

= 1133 – 2316 – 1754 + 5694

= (1133 + 5694) – (2316 + 1754 )

= 6827 – 4070

= 2757

Calculation:

Let x = 0.0181818....

⇒ 10x = 0.1818....      ----eq (1)

⇒ 1000x = 18.1818....      ----eq (2)

Now, eq (2) - eq (1)

⇒ 1000x - 10x = 18.1818... - 0.1818...

⇒ 990x = 18

⇒ x = 18/990

⇒ x = 1/55

∴ The fraction of \(0.0\overline {18} \) is 1/55

Shortcut Trick

\(0.\overline {ab} = ab/99\)

ab¯" role="presentation" style="display: inline; position: relative;" tabindex="0">\(0.0 \:\overline {ab} = ab/990\)

⇒ ab¯" role="presentation" style="display: inline; position: relative;" tabindex="0">\(0.0\overline {18} = 18/990\)

⇒ 2/110 = 1/55

∴ The fraction of \(0.0\overline {18} \) is 1/55.
ab¯" role="presentation" style="display: inline; position: relative;" tabindex="0">ab" id="MathJax-Element-5-Frame" role="presentation" style="position: relative;" tabindex="0">ab ab ab = ab/99

Calculations:

0.36 of 52.5 + ? of 35 = 57.4

⇒ 18.9 + ? of 35 = 57.4

⇒ ? of 35 = (57.4 − 18.9)

⇒ ? = 38.5/35 

⇒ ? = 1.1

Given:

 {(.98)3 + (0.02)3 + 3 × 0.98 × 0.02 – 1}

Concept used:

(a + b)3 = a3 + b3 + 3ab(a + b)

Calculation:

{(.98)³ + (0.02)³ + 3 × 0.98 × 0.02 – 1

⇒ [(.98)³ + (0.02)³ + 3 × 0.98 × 0.02(0.98 + 0.02)} – 1]

Now, first term is of the form (a + b)3 where a = .98 and b = 0.02

⇒ (0.98 + 0.02)³ – 1 = 1 – 1 = 0

∴ The value is 0.

Concept used:

BODMAS 

Calculation:

= (9.6 × 3.6 ÷ 7.2 + 10.8 of \(\frac{1}{{18}}\) - \(\frac{1}{{10}}\))

= (9.6 × 3.6 ÷ 7.2 + 0.6  - \(\frac{1}{{10}}\))

= (9.6 × \(\frac{1}{2}\) + 0.6  - \(\frac{1}{{10}}\))

= (4.8 + 0.6  - \(\frac{1}{{10}}\))

= \(\frac{48\ +\ 6\ - \ 1}{10}\)

= \(\frac{53}{10}\)

= 5.3

Answer is 5.3

Given:

The given expression = (1.6)3 - (0.9)3 - (0.7)3

Formula used:

If a + b + c = 0, then a³ + b³ + c³ = 3abc

Calculation:

(1.6)3 - (0.9)3 - (0.7)3

= (1.6)3 + (- 0.9)3 + (- 0.7)3

= 3 × 1.6 × (- 0.9) × (- 0.7)  [∵ 1.6 - 0.9 - 0.7 = 0]

= 3.024

∴ The value of the given expression is 3.024