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

Given: 

⇒ 3.4 + 2.025 + 9.36 - 3 × (4.1003) = 3 - p

Concept used: 

Calculation:

⇒ 3.4 + 2.025 + 9.36 - 3 × (4.1003) = 3 - p

⇒ 3.4 + 2.025 + 9.36 - 12. 3009 = 3 - p

⇒ 14. 785 - 12. 3009 = 3 - p

⇒ 2.4841 = 3 - p

⇒ p = 0. 5159

∴ Option 3 is correct.

Given:

Expression: 6893.5 × 603.3 × 0.3019

Formula used:

For two products to be equal, the overall decimal place shifts must balance out.

Calculations:

Original expression's decimal shifts (relative to integer):

6893.5 (1 place left) × 603.3 (1 place left) × 0.3019 (4 places left)

Total left shift = 1 + 1 + 4 = 6 places.

Let's examine the options for a total 6-place left shift:

Option 1: 6.8935 (4 left) × 60.33 (2 left) × 30.19 (2 right)

Net shift = 4 + 2 - 2 = 4 places left. (Incorrect)

Option 2: 6.8935 (4 left) × 6.033 (3 left) × 301.9 (1 right)

Net shift = 4 + 3 - 1 = 6 places left. (Correct)

Wait, let me re-evaluate the shifts from the original numbers, not relative to integers. This is about comparing the original product to the product of the options.

Let P = 6893.5 × 603.3 × 0.3019

Option 1: 6.8935 × 60.33 × 30.19

(6893.5 / 1000) × (603.3 / 10) × (0.3019 × 100)

= P × (1/1000) × (1/10) × 100 = P × (100/10000) = P / 100 (Incorrect)

Option 2: 6.8935 × 6.033 × 301.9

(6893.5 / 1000) × (603.3 / 100) × (0.3019 × 1000)

= P × (1/1000) × (1/100) × 1000 = P × (1000/100000) = P / 100 (Incorrect)

Option 3: 68.935 × 6033 × 3.019

(6893.5 / 100) × (603.3 × 10) × (0.3019 × 10)

= P × (1/100) × 10 × 10 = P × (100/100) = P × 1 (Correct)

Option 4: 689.35 × 603.3 × 301.9

(6893.5 / 10) × 603.3 × (0.3019 × 1000)

= P × (1/10) × 1 × 1000 = P × (1000/10) = P × 100 (Incorrect)

∴ The correct answer is option 3.

Alternate Method 

Given:

Expression: 6893.5 × 603.3 × 0.3019

Formula used:

When we shift the decimal point in all numbers such that the overall scaling factor remains 1, the product stays the same.

Calculation:

Original numbers:

6893.5 = 68.935 × 100

603.3 = 6033 ÷ 10

0.3019 = 3.019 ÷ 10

Let's adjust them oppositely to balance the product:

6893.5 ÷ 100 = 68.935   ÷100

603.3 × 10 = 6033   ×10

0.3019 × 10 = 3.019   ×10

Overall scaling factor:

⇒ (÷100) × (×10) × (×10) = ÷100 × 100 = 1

Therefore, the product remains the same.

∴ The correct answer is option (3): 68.935 × 6033 × 3.019.

Given:

79.63 + 963.8 - x + 7.953 = 18.732

Calculations:

⇒ x = (79.63 + 963.8 + 7.953) - 18.732

⇒ x = 1051.383 - 18.732

⇒ x = 1032.651

∴ The correct answer is option (3).

Given:

The value of 

Formula Used:

Calculation:

Here, a = 0.96 and b = 0.1 .

Using the formula:

⇒

⇒ 0.96 - 0.1

⇒ 0.86

The correct answer is option 3.

Given:

The expression to evaluate is $\sqrt{0.99 × 0.99 × 0.99}$

Formula Used:

Calculations:

Let the given expression be E.

E =

E =

We can also write this as: E =

Let's approximate the value of E:

We know that  is slightly less than 1, but very close to 1. Approximately, .

So, E ≈ 0.99 × 0.995

E ≈ 0.98505

Now, let's evaluate the given options:

1. 0.99 × 0.33 = 0.3267

2. 0.33 × 0.33 × 0.33 = (0.33)³ = 0.035937

3. 0.99 × 0.99 × 0.99 = (0.99)³ = 0.970299

4. 0.33

Comparing our calculated value of E ($≈ 0.98505$) with the options:

Difference with Option 1: $|0.98505 - 0.3267| ≈ 0.658$

Difference with Option 2: $|0.98505 - 0.035937| ≈ 0.949$

Difference with Option 3: $|0.98505 - 0.970299| ≈ 0.014751$

Difference with Option 4: $|0.98505 - 0.33| ≈ 0.655$

The smallest difference is with Option 3 (0.970299).

Also, it's important to note the general property: For a number 'x' between 0 and 1 (0

x³ 3/2 

In our case, 0.99³ 3/2 

0.970299 3/2 

Only option 3 falls within the correct magnitude range and is numerically closest to our calculated value.

Therefore, the expression is closest to 0.99 × 0.99 × 0.99.

Since,

a2 - b2 = (a - b) ( a + b)

⇒ 0.9 × 0.7 = 0.63

∴ Answer is 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

⇒ ? = 10

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:

⇒ ? = 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  is 1/55

Shortcut Trick

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⇒ ">ab¯" role="presentation" style="display: inline; position: relative;" tabindex="0">

⇒ 2/110 = 1/55

∴ The fraction of  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">abab = 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(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.

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

Concept used:

BODMAS 

Calculation:

= (9.6 × 3.6 ÷ 7.2 + 10.8 of  - )

= (9.6 × 3.6 ÷ 7.2 + 0.6  - )

= (9.6 ×  + 0.6  - )

= (4.8 + 0.6  - )

= 

= 

= 5.3

Answer is 5.3