# 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 + c– 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} \$

#### 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.

#### 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

#### 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