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

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.

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

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

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

We know that the formula of (a+b)^{ 2} = a^{2} + b^{2} + 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