Problems on Decimal Fraction

Problems on Decimal Fraction

Learn and practice Problems on Decimal Fraction with easy explaination and shortcut tricks. All questions and answers on Decimal Fraction covered for various Competitive Exams.

Solve Problems:

1) Find the missing term of the given expression:
18.834 + 818.34 -? = 618.43

  1. 217.644
  2. 218.744
  3. 217.744
  4. 217.844
View Answer

Answer: B

Explanation:

18.834 + 818.34 – ? = 618.43

Or, 18.834 + 818.340 – 618.43 =?

837.174 – 618.430 = 218.744

2) What is the value of (25.732)2 – (15.732)2?

  1. 414.64
  2. 414.256
  3. 414.128
  4. 414.52
View Answer

Answer: A

Explanation:

We know that, a2 – b2 = (a+b) (a – b)

Or, (25.732)2 – (15.732)2 = (25.732 + 15.732) (25.732 – 15.732)

Or, the value = 41.464 * 10 = 414.64

3) Approximate value of 0.4*0.4 + 0.04*0.04 + 0.04 is

  1. 0.20
  2. 0.38
  3. 0.16
  4. 0.46
View Answer

Answer: A

Explanation:

0.4 * 0.4 = 0.16

0.04*0.04 = 0.0016

Hence, 0.16+0.0016+0.04 = 0.2016, or the approximate value = 0.20

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4) The value of 0.3̅4̅2̅1 is

  1. 3421/10000
  2. 3421/9.999
  3. 3421/9999
  4. None of these
View Answer

Answer: C

Explanation:

Solution 1:

We have 0.3̅4̅2̅1 = 0.342134213421…….. (i)

Multiply both sides by 10, we get

10 * 0.3̅4̅2̅1 = 3.421………………. (ii)

But on comparing both equations, the repeating number should be the same after the decimal point.

So, multiply equation 2 by 1000, we get
10000* 0.3̅4̅2̅1 = 3421.342134213421…. ……. (iii)

Now subtract equation i from iii, we get
(10000 – 1) * 0.3̅4̅2̅1 = 3421.342134213421… – 0.342134213421…..
Or, 9999 * 0.3̅4̅2̅1= 3421
Or, 0.3̅4̅2̅1 = 3421/9999

Solution 2:

Quick method:

Note: the period of 0.7̅ is 7, so the numerator of the fraction is 7, and there is one digit in the period, the denominator will have one nine.

Therefore, the vulgar fraction = 7/9

Similarly, the period of 0.3̅4̅2̅1 is 3421, so the numerator of the fraction is 3421, and there is four digit in the period, the denominator will have four nine.

Hence, the vulgar fraction will be 3421/9999.

5) In the given expression (1.05)2 *x = 44.1, find the value of x.

  1. 40.00
  2. 40.01
  3. 42.00
  4. 42.01
View Answer

Answer: A

Explanation:

Given, (1.05)2 * x =44.1
Or, x = 44.1/ (1.05)2 = 44.1/ (1.05 * 1.05)
Hence, x = 40.00

6) If 12276 /1.55 = 7920, what is the value of 122.76/15.5?

  1. 7.097
  2. 7.92
  3. 79.2
  4. 79.02
View Answer

Answer: B

Explanation:

Note: If numerator and denominator have the different number of decimal place, we have to equate both numbers of figures in decimal part by putting zeros, and then remove the decimals.

i.e., 12276/1.55 is equals to 1227600/155 = 7920.
Similarly, 122.76/ 15.5 = 12276/1550 = 7.92

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7) Find the value of the given expression
11.121/ 0.11 + 111.21/0.11

  1. 1022.121
  2. 1111.200
  3. 1202.121
  4. 1112.100
View Answer

Answer: D

Explanation:

Note: the mathematical expressions follow BODMAS rule for priority.

So, division expression will be evaluated first
i.e., 11.121/0.11 = 11121/110 = 101.1
And, 111.21/0.11 = 11121/11 = 1011
Now, addition of both numbers = 1011 + 101.1 = 1112.1

8) 54.327 * 357.2 * 0.0057 is the same as

  1. 54327 * 3572 * 0.0000057
  2. 5.4327 * 3.572 * 0.57
  3. 5.4327 * 3.572 * 5.7
  4. None of these
View Answer

Answer: C

Explanation:

As per the question: 54.327 * 357.2 * 0.0057 = 110.611…….. (i)
Option a: 54327 * 3572 * 0.0000057 = 1106.11….. (ii)
Option b: 5.4327 * 3.572 * 0.57 = 11.06……… (iii)
Option c: 5.4327 * 3.572 * 5.7 = 110.611………… (iv)
The value of equation i and iv is same. So, the answer is option C.

9) The given expression (11.98 * 11.98 + 11.98 * x + 0.02 * 0.02) will be a perfect square for x equal to

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

Answer: C

Explanation:

We know that the formula of (a+b) 2 = a2 + b2 + 2ab
Let a = 11.98, and b = 0.02
Here, the expression should be 11.98*11.98 + 0.02*0.02 + 2*11.98 * 0.02
But the actual expression is 11.98 * 11.98 + 0.02*0.02 + 11.98 * x
Compare both the expression, we get x = 2*0.02 = 0.04

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10) The value of [2.75*2.75*2.75 – 2.25*2.25*2.25]/[2.75*2.75+2.75*2.25+2.25*2.25] is

  1. 0.30
  2. 0.50
  3. 3
  4. 5
View Answer

Answer: B

Explanation:

Given expression

X= [(2.75)3 – (2.25)3]/ [(2.75)2+ 2.75 * 2.25 + (2.25)2]
We have, a3 – b3 = (a-b) (a2 + ab + b2)

Therefore, x = [(2.75 – 2.25) {(2.75)2 + 2.75*2.25 + (2.25)2}]/ [(2.75)2 + 2.75 *2.25 + (2.25)2]
Or, x = 2.75 – 2.25 = 0.50

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