Important Formulas: Fractions, Decimals, Percents (FDP) | Quantitative for GMAT PDF Download

1. Decimal Fractions:

   Fractions in which denominators are powers of 10 are known as decimal fractions.

    

   Thus,	1	= 1 tenth = .1;	1	= 1 hundredth = .01;
   	10		100

    

   99	= 99 hundredths = .99;	7	= 7 thousandths = .007, etc.;
   100		1000

2. Conversion of a Decimal into Vulgar Fraction:

   Put 1 in the denominator under the decimal point and annex with it as many zeros as is the number of digits after the decimal point. Now, remove the decimal point and reduce the fraction to its lowest terms.

    

   Thus, 0.25 =	25	=	1	;       2.008 =	2008	=	251	.
   	100		4		1000		125

3. Annexing Zeros and Removing Decimal Signs:

   Annexing zeros to the extreme right of a decimal fraction does not change its value. Thus, 0.8 = 0.80 = 0.800, etc.

   If numerator and denominator of a fraction contain the same number of decimal places, then we remove the decimal sign.

    

   Thus,	1.84	=	184	=	8	.
   	2.99		299		13

4. Operations on Decimal Fractions:

   1. Addition and Subtraction of Decimal Fractions: The given numbers are so placed under each other that the decimal points lie in one column. The numbers so arranged can now be added or subtracted in the usual way.

   2. Multiplication of a Decimal Fraction By a Power of 10: Shift the decimal point to the right by as many places as is the power of 10.

      Thus, 5.9632 x 100 = 596.32;   0.073 x 10000 = 730.

   3. Multiplication of Decimal Fractions: Multiply the given numbers considering them without decimal point. Now, in the product, the decimal point is marked off to obtain as many places of decimal as is the sum of the number of decimal places in the given numbers.

      Suppose we have to find the product (.2 x 0.02 x .002).

      Now, 2 x 2 x 2 = 8. Sum of decimal places = (1 + 2 + 3) = 6.

       .2 x .02 x .002 = .000008

   4. Dividing a Decimal Fraction By a Counting Number: Divide the given number without considering the decimal point, by the given counting number. Now, in the quotient, put the decimal point to give as many places of decimal as there are in the dividend.

      Suppose we have to find the quotient (0.0204 ÷ 17). Now, 204 ÷ 17 = 12.

      Dividend contains 4 places of decimal. So, 0.0204 ÷ 17 = 0.0012

   5. Dividing a Decimal Fraction By a Decimal Fraction: Multiply both the dividend and the divisor by a suitable power of 10 to make divisor a whole number.

      Now, proceed as above.

       

      Thus,	0.00066	=	0.00066 x 100	=	0.066	= .006
      	0.11		0.11 x 100		11

5. Comparison of Fractions:

   Suppose some fractions are to be arranged in ascending or descending order of magnitude, then convert each one of the given fractions in the decimal form, and arrange them accordingly.

    

   Let us to arrange the fractions	3	,	6	and	7	in descending order.
   	5		7		9

    

   Now,	3	= 0.6,	6	= 0.857,	7	= 0.777...
   	5		7		9

    

   Since, 0.857 > 0.777... > 0.6. So,	6	>	7	>	3	.
   	7		9		5

6. Recurring Decimal:

   If in a decimal fraction, a figure or a set of figures is repeated continuously, then such a number is called a recurring decimal.

   n a recurring decimal, if a single figure is repeated, then it is expressed by putting a dot on it. If a set of figures is repeated, it is expressed by putting a bar on the set.

    

   Thus,	1	= 0.333... = 0.3;	22	= 3.142857142857.... = 3.142857.
   	3		7

   Pure Recurring Decimal: A decimal fraction, in which all the figures after the decimal point are repeated, is called a pure recurring decimal.

   Converting a Pure Recurring Decimal into Vulgar Fraction: Write the repeated figures only once in the numerator and take as many nines in the denominator as is the number of repeating figures.

    

   Thus, 0.5 =	5	; 0.53 =	53	; 0.067 =	67	, etc.
   	9		99		999

   Mixed Recurring Decimal: A decimal fraction in which some figures do not repeat and some of them are repeated, is called a mixed recurring decimal.

   Eg. 0.1733333.. = 0.173.

   Converting a Mixed Recurring Decimal Into Vulgar Fraction: In the numerator, take the difference between the number formed by all the digits after decimal point (taking repeated digits only once) and that formed by the digits which are not repeated. In the denominator, take the number formed by as many nines as there are repeating digits followed by as many zeros as is the number of non-repeating digits.

   Thus, 0.16 =	16 - 1	=	15	=	1	;   0.2273 =	2273 - 22	=	2251	.
   	90		90		6		9900		9900

Percentage Formula

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.
Percentage formula = (Value/Total value) × 100
Example: 2/5 × 100 = 0.4 × 100 = 40 per cent

How to calculate the percentage of a number?

To calculate the percentage of a number, we need to use a different formula such as: P% of Number = X
where X is the required percentage.
If we remove the % sign, then we need to express the above formulas as;
P/100 * Number = X

Example: Calculate 10% of 80.
Let 10% of 80 = X
10/100 * 80 = X
X = 8

Percentage Difference Formula

If we are given with two values and we need to find the percentage difference between these two values, then it can be done using the formula:

For example, if 20 and 30 are two different values, then the percentage difference between them will be:
% difference between 20 and 30 =

Percentage Increase and Decrease

The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.

% increase = [(New number – Original number)/Original number] x 100

where,
increase in number = New number – original number
Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100. 

% decrease = [(Original number – New number)/Original number] x 100

Where decrease in number = Original number – New number
So basically if the answer is negative then there is a percentage decrease.

Percentage Chart