Percentages

The word “Percent” comes from the Latin word “per centum” and the Latin word “centum” means 100. Percentage actually means “out of 100” and it is represented by the symbol (%). The symbol can be efficiently used to represent a fraction that has a common denominator of 100. For instance if there are 29 girls in a class which has a strength of 100, then you need not represent it as 29 out of 100 students are girls as you can represent it in terms of percent and say 29% of the students in the class are girls.

How to Convert Decimal into Percentage

The box on the left has 75 of the 100 squares blue, so 75/100, or 0.75 of the box is green.

To convert from decimal to percentage, multiply the decimal by 100

In other words, to convert decimal into percent, shift the decimal point two places to the right of the number and add a ‘%’ sign.

For example 1/4 = 25/100. In percentage this will be 25%
1/4 can be written as a decimal as 0.25
1/4, 25% and 0.25 mean the same.

In order to convert 0.25 in percentage, first multiply the decimal by 100 and then put a ‘%’ sign beside the number.

This is how any decimal number is converted into percentage.

Examples:
0.65 x 100 = 65 %
0.465 x 100 = 46.5 %
In order to convert a fraction into percentage, first the fraction is converted into a decimal, then into percentage.

Examples:
3/5 = 0.60 = 60%

How to Convert Percentage into Decimal

In the figure above, 30 of the 100 squares are blue.

It means 30 per 100 or 30/100.
If number 30 is divided by 100, we get 0.3 which is a decimal number. In order to convert percentage to decimal, just divide by 100 and also remove the ‘%’ sign. In other words, to convert percent into decimals, shift the decimal point two places to the left.

Examples:
50/100 = 0.5
65/ 100= 0.65
7.5 / 100 = 0.075

Moreover, percent always means per 100 and therefore it always has 100 as the divisor as 35% actually means 35/100. In that way, when you say 100% it is actually 100/100 i.e, 1. In fact, 100% of any number is exactly that number. Similarly, 200% means twice the number.

Solved Problems:

Question:

The cost of a T-shirt is $60 in a showroom. However, to clear old stocks, the showroom suddenly announces a discount rate of 20%. Then what will be the cost of the T-shirt?

Answer:
The cost of the T-shirt after applying the discount will be $48
20% of $60 = 20/100 x 60 = 12

Therefore, 20% of $60 is $12
After the discount is in effect, the cost of the T-shirt will be $60 – $12 = $48

Question:
John got 80 in Mathematics in his last exam. This time John practiced Mathematics even harder and his marks increase by 5% compared to last time. What was John’s marks this time?

Answer:
John got 84 in Mathematics
5% of 80 = 5/100 x 80 = 4.

Therefore, 5% of 80 is 4.
After a 5% increase in the number, this time John got 80 + 4 = 84.

Question:
4 out of 5 people sleep on their right. Find out the percentage of this.

Answer:
80%

First, we will have to find out what 4 out of 5 of one hundred is? The formula could be  (Amount ÷ Total) × 100
= 4/5 × 100
= 0.8 × 100
= 80%

Therefore, 80 % people sleep on their right.

Question:
The railway board constructed a pillar 130 m long to stand a bridge but later on it was realized that it needed to be longer. The engineers studied the pillar and suggested a further 10% increase in its size. What would be the size after the pillar is reconstructed?

Answer:
The size of the pillar will be 143m.
10% of 130m = 10/100 x 130m = 13m.

Therefore, 10% of 130m is 13m.
Therefore, the total size of the pillar after it is reconstructed will be 130m + 13m = 143m

Question:
The profit of a company during the first quarter was $14,000. However, in the second quarter there was 4% decrease in the profit margin. What was the profit in the 2nd quarter?

Answer:
After the reduction in the profit, the profit in the 2nd quarter was $13440.
4% of $14,000 = 4/100 x 14,000 = $560

Therefore, 4% of $14,000 is $560
Therefore, the profit in the 2nd quarter is $14,000 – $560 = $13440

Question:
In an election, 2,268 people voted for George, 8,820 voted for Anna and 1,512 voted for Stuart. What is the percentage of votes that each of the candidate received?

Answer:
First, calculate the total number of votes. It is 2268 + 8820+1512 = 12600

The total number of votes is 12,600.

Now, the percentage of votes George received
(2268/ 12600) x 100
= 0.18 x 100
= 18 %

Similarly, the percentage of votes Anna received  
(8820/ 12600) x 100
= (8820 / 12600) x 100
= 0.7 x 100
= 70 %

Finally, the percentage of votes Stuart received:
(1512 / 12600) x 100
= (1512 / 12600) x 100
= 0.12 x 100
= 12 %

Therefore, George, Anna and Stuart have received 18%, 70% and 12% votes respectively.

Question:
Find out how much interest will $2000 earn in 1year at an annual interest rate of 8%.

Answer:
As you know 8% = 8/100
= (8/100) x 2000
= 0.08 X 2000 = 160

Therefore, the answer is $160

Question:
What is the discount amount if a car costing $9000 is discounted at 9%?

Answer:
In order to find the discount, the formula is:
Discount = Cost x Rate of Discount
As, 9% is = 0.09

Therefore,  Discount = 9000 x 0.09 = 810
The discount amount is = $ 810

Question:
If 23 % of a number is 46, find the number?

Answer:
Let the number be ‘a’

Therefore, 23% of a = 46
(23/100) x a = 46
a = 46 x 100 / 23
a = 200.

The number is 200.

Question:
In an examination, Betty secured 372 marks. If she secured 62% marks, find the maximum marks.

Answer:
Let the maximum marks be ‘a’.

Betty’s marks = 62% of a
Betty’s secured 372 marks

Therefore, 62 % of a = 372
or, (62/100) x a = 372
or, a = (372 /62) x 100
x = 600

Hence, the maximum marks is 600.

Question:
In an election, a candidate got 60% of the total valid votes. 15% of the total votes were declared invalid. If the total number of votes is 500,000, find the number of valid votes polled in favor of the candidate.

Answer:
Total number of invalid votes = 15% of 500000
= 15 / 100 x 500000
= 75000

Thus, total number of valid votes polled = 500000 – 75000 = 425000

Therefore, percentage of valid votes polled in favor of the candidate:
= 60% of 425000
= 60/100 x 425000
= 255000

Thus, the number of valid votes polled in favor of the candidate is 255000.