# Percentage

# Percentage

**P****ercentages are an important part of our everyday lives. We use percentages in different areas. Such as % discount in shopping malls, % rainfall of the year, bank interest rates, % housing loan, % of the girl passed in 10th class, % rate of petrol and diesel. Percentages are a useful way of comparing fractions with different denominators. Percentages give information which is often easier to understand than fractions.**

**Example:**** of the total number of students in the class are male, is quite difficult to interpret, while the statement 45% of the total number of students in the class are male is easier to understand**

**Meaning of Percentage:**

**Percent****: The word percent is derived from the Latin word ‘percentum’ which means ‘per hundred’.**

**Percentage****: Percentage are numerators of fractions with denominator 100. The percentage is denoted by the symbol ‘%’ i.e., 1 % means 1 out of 100. It can be written as 1%= 1/100=0.01**

**Example:**** When we say Rakesh gives 20% of his income as income tax, this means that he gives ₹ 20 out of every hundred rupees of his income.**

**To understand this let us consider the following example.**

**Aniket is fond of collecting souvenirs. He collected 100 souvenirs from different countries. From the table can you tell the percentage of souvenirs of any country?**

**Percentages when the total is not a hundred**

**In such cases, we need to convert the fractions to an equivalent fraction with denominator 100.
Any fraction can be expressed into a percentage by multiplying it by 100.**

**We multiply the fraction by 100/100. This does not change the value of the fraction.**

**Example: Write as a percent. **

**=****×= (× 100) % = ( )%=12%**

**Example: Write as a percent.**

** = x = (****× 100) % = (**** )%=5%**

**Example: There are 50 students in class VII, and 35 go to the picnic. Calculate the percentage of the number of students who go to the picnic?**

**35 students of the 50 go to the picnic.**

**Percentage of the number of students in class VII = ×**

**= (****× 100) % =**** = 70%**

**So, 70% of the students go to the picnic**

**Converting fractional numbers to Percentage**

**To convert a fractional number into percentages, multiply the fraction by 100 and put the % sign.**

**Example: Convert the fractional number **** into percent.**

** = **** ****× **** = (**** ****× 100)%= ( )%= 6%**

**Example: Convert the fractional number into percent.**

** = **** ****× **** ****= (**** ****× 100)%= ( )%=12.5%**

**Converting Decimals to Percentage**

**To convert a decimal number into a percentage, multiply the decimal number by 100 and put the % sign.**

**Express each of the following decimal number into percent.**

**(i) 0.55 (ii) 0.07 (iii) 2.2**

**(i) 0.55 = 0.55 × 100% = × 100% = 55 %**

**(ii) 0.07 = 0.07 × 100% = × 100% = 7%**

**(iii) 2.2 = 2.2 × 100% = × 100% = 220%**

**Converting Percentages to fraction or decimals**

**To convert a percentage into a fraction or a decimal, divide it by 100%.**

**Express 140 % percentage into a fraction.**

**140 % = = = **

**Express 140 % percentage into a decimal.**

**140 % = = 1.40**

**Express 3 % percentage into a decimal.**

**3 % = = 0. 03**

**Express 20 % percentage into a fraction.**

**20 % = = **

**Percentage – Concept of Whole**

**The percentage is also used as the concept of the whole. Suppose if we add parts together it always gives a whole (100%). Similarly, if the whole is divided into parts it combines and gives you a whole or 100%.**

**Example:**** As we know the air is a mixture of gases and that gases are present in the atmosphere in different percentages. When we add the percentage of different gases in the atmosphere we get 100%**

**So, if we are given one part, we can always find out the other part. Suppose Rashmi has 1 whole pizza, it consists of 8 parts out of these Rashmi gives 4 parts to her brother, we can always find out the remaining parts of the pizza.**

**Example: In a school, 30% students are girls, find the percentage of boys. **

**Total number of students in the school = 100%**

**Percentage of girls in a school = 30%**

**The percentage of boys in a school = Total number of students in the school (100%) – Percentage of girls in a school**

**The percentage of boys in a school = 100% – 30% = 70%**

**Example: 68% candidates appear for the JEE exam. What percent of candidates not appear for the exam?**

**Total number of candidates= 100%**

**Candidates appear for the JEE exam = 68%**

**Percent of candidate did not appear for the exam = Total number of candidates (100%) – Candidates appearing for the JEE exam**

**Percent of candidate did not appear for the exam = 100% – 68% = 32%**