Short Theoretical Questions
1. What is meant by percentage?
Answer: Percentage means a fraction out of 100. It is written using the symbol (%).
2. Why is the denominator 100 used in percentages?
Answer: Because “per cent” means “per hundred”, so all percentages are expressed out of 100.
3. How are fractions and percentages related?
Answer: A percentage is a fraction whose denominator is 100.
4. How can a fraction be converted into a percentage?
Answer: By multiplying the fraction by 100.
5. How can a percentage be converted into a fraction?
Answer: By writing it over 100 and simplifying.
6. What is meant by “per cent”?
Answer: “Per cent” means “out of every 100”.
7. Why are percentages useful for comparison?
Answer: Because they convert different quantities into a common base (100), making comparison easy.
8. What is meant by percentage of a quantity?
Answer: It means finding a part of a quantity out of 100.
9. Can percentages be more than 100?
Answer: Yes, it means the value is greater than the original quantity.
10. How are decimals related to percentages?
Answer: A percentage can be converted into decimal by dividing by 100.
Long Theoretical Questions
1. Explain the concept of percentage with examples.
Answer: Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol (%). For example, 50% means 50 out of 100 or half. Similarly, 25% means 25 out of 100 or one-fourth. Percentages are widely used in marks, discounts, and daily life calculations.
2. Describe the methods of converting fractions into percentages.
Answer: There are two main methods:
- Multiply the fraction by 100.
- Convert the fraction into an equivalent fraction with denominator 100.
For example, .
3. Explain why percentages are preferred over fractions in daily life.
Answer: Percentages are easier to compare because they are always expressed out of 100. For example, comparing 26.47% and 28.88% is easier than comparing fractions like 9/34 and 13/45. Hence, percentages make understanding and comparison simple.
4. Explain how to find the percentage of a given quantity.
Answer: To find the percentage of a quantity, multiply the percentage by the quantity and divide by 100.
For example, 25% of 200 = (25/100 × 200) = 50. This method helps in solving problems related to marks, money, and measurements.
5. Explain the relationship between fractions, decimals, and percentages.
Answer: Fractions, decimals, and percentages represent the same value in different forms. A fraction can be converted into a decimal by division, and into a percentage by multiplying by 100. For example,
Thus, all three forms are interconnected and can be converted into each other easily.
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