How To Solve Numbers, Decimal And Fractions Questions Quickly

How to Solve Numbers, Decimal and Fractions Quickly :-

A fraction where the denominator (the bottom number) is a power of ten (such as 10, 100, 1000, etc).

We can write decimal fractions with a decimal point (and no denominator), which make it easier to do calculations like addition and multiplication on fractions.

Examples: 

 \frac{7}{10} \  is a decimal fraction and it can be shown as 0.7

 \frac{43}{100} \ is a decimal fraction and it can be shown as 0.43

 \frac{88}{1000} \  is a decimal fraction and it can be shown as 0.088

How To Solve Quickly Number, Decimal and Fraction: 

It represents a part of a whole or more generally, any number of equal parts. If a unit is divided into any number of equal parts, then one or more of these parts is termed as a fraction of the unit.

The numerator in a fraction represents a number of equal parts and denominator (≠0) represents how many of those parts make up a unit or a whole.

The value of fraction (x/y) = 1, if numerator = denominator
The value of fraction is zero,if numerator=0 and denominator ≠0 
The value of fraction is infinity,if the denominator=0
The value of fraction remains unchanged,even if the numerator and denominator are multiplied or divided by same number

Pure recurring decimal: In a decimal fraction, if all the numbers after decimal point repeat, then it is called as pure recurring decimal. 
Mixed recurring decimal: In a decimal fraction, if some numbers are repetitive and some are not, then it is called as mixed recurring decimal. 

Basic Concept To Solve Number, Decimals and Fractions Questions Quickly : 

(Must Remember) 

1) (a – b)2 = (a2 + b2 – 2ab)
2) (a + b)2 = (a2 + b2 + 2ab)
3) (a + b) (a – b) = (a2 – b2 ) 
4) (a3 + b3) = (a + b) (a2 – ab + b2) 
5) (a3 – b3) = (a – b) (a2 – ab + b2)
6) (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)
7) (a3 + b3 + c3 – 3abc) = (a + b + c) (a2 + b2 + c2 – ab – bc – ac)

Question 1

(i) Convert 0.737373… into vulgar fraction?

Options

(a)  \frac{73}{99} \

(b)  \frac{77}{99} \

(c)  \frac{73}{90} \

(d)  \frac{73}{900} \

Correct Answer: Option A

Explanation:

In a decimal fraction, if there are n numbers of repeated numbers after a decimal point, then just write one repeated number in the numerator and in denominator take n number of nines equal to repeated numbers you observe after the decimal point.
0.737373… is written as  \frac{}{}0.\overline{73} .

How To Solve Number, Decimals and Fractions Quickly Questions

Question 2

(ii)Find the number of zeros in 2145 x 5234 

Options

(a) 145
(b) 234
(c) 10
(d) None of these.

Correct Options: A

Explanations

we have to look for  the pairs of 2x 5, so the maximum pairs we can form are 145 because we have the  maximum power  of 2 is 145 , so the number of zeros  in this case are 145.

Questions 3

(iii)Find the number of zeros at end of
5 x 10 x 15 x 20 x 25 x 30 x 35…………………………………… x 240 x 245 x 250

Options

(a) 30
(b) 47
(c) 50
(d) 48

Correct Options: B

Explanations

We can take 5 common out of this expression and write it as
550 (1 x 2 x 3 x 4……………………………………  x 49 x 50)
550 (50!)
To find number of zeros we first find
Maximum power of 2 in 50!
[  \frac{50}{2} \ ] + [  \frac{50}{2^2} \ ] + [  \frac{50}{2^3} \ ] + [  \frac{50}{2^4} \ ] + [  \frac{50}{2^5} \ ] + ………. 
= 25 + 12 + 6 + 3 +1= 47
Maximum power of 5 in 50!

 \frac{50}{5} \ + [  \frac{50}{5^2} \ ] + [  \frac{50}{5^3} \ ]
= 10 + 2= 12

Thus maximum power of 5 present in given expression is 62 and maximum power of 2 present in given expression is 47. Hence number of zeros will be 47.

Read Also: Formula for Numbers, Decimal and Fractions question