Decimals and percentages are fundamental concepts used in mathematics to represent and compare numbers. Understanding decimals and percentages is crucial since they are used frequently in a variety of real-world contexts, including calculating discounts, interest rates, and proportions. In this article, we'll examine the principles of decimals and percentages and provide ten examples from everyday life to illustrate their potential applications.

## Definition of Decimals:

Numbers between two consecutive whole numbers can be expressed using decimals. They are used to more conveniently and succinctly represent fractions. The fractional portion is distinguished from the whole number portion by the decimal point. For instance, the decimal 2.75 denotes two whole units and 75.000ths.

### Conversion between Decimals and Fractions:

Determine the place value of each digit in a decimal before converting it to a fraction. For instance, the fraction 75/100 or 3/4 can be used to represent the decimal 0.75. Like with decimals, fractions can be generated by dividing the numerator by the denominator. For instance, the decimal 0.6 can be used to represent the fraction 3/5.

#### Definition of Percentages:

Percentages are a way of expressing parts of a whole in terms of hundredths. The symbol "%" represents a percentage. For example, the percentage 50% means 50 out of 100 or one-half.

Conversion between Percentages and Decimals:

To convert a percentage to decimal form, divide the percentage by 100. For instance, 0.75 is what 75% would be in decimal form. In contrast, a decimal will become a percentage when multiplied by 100. For instance, the decimal 0.6 can be used to represent 60%.

Now let's look at ten examples that demonstrate the application of decimals and percentages:

Example 1: Convert 0.4 to a fraction.

Solution: The decimal 0.4 can be written as the fraction 4/10, which simplifies to 2/5.

Example 2: Convert 3/5 to a decimal.

Solution: Divide 3 by 5 to get the decimal 0.6.

Example 3: Convert 60% to a decimal.

Solution: Divide 60 by 100 to get the decimal 0.6.

Example 4: Add 0.75 and 0.3.

Solution: The sum of 0.75 and 0.3 is 1.05.

Example 5: Find 25% of 80.

Solution: Multiply 80 by 25% (or 0.25) to get 20.

Example 6: Convert 2.5 to a percentage.

Solution: Multiply 2.5 by 100 to get the percentage 250%.

Example 7: Subtract 0.4 from 1.

Solution: The difference between 1 and 0.4 is 0.6.

Example 8: Find 20% more than 150.

Solution: Multiply 150 by 20% (or 0.20) and add the result to 150. The answer is 180.

Example 9: Convert 3/8 to a percentage.

Solution: Divide 3 by 8 and multiply the result by 100 to get the percentage 37.5%.

Example 10: Find 40% of a number is 120. What is the number?

Solution: Divide 120 by 40% (or 0.40) to find the number, which is 300.

These examples demonstrate how decimals and percentages can be applied to computations in the real world. Students who understand these concepts can use them in a variety of situations, such as discount calculations, proportional comprehension, data analysis, and solving real-world percentage and decimal problems.

To sum up, decimals and percentages are very important in mathematics and have many uses in our daily lives. For problem-solving and precise calculation, it is essential to comprehend their concepts and be able to convert between them. Students can build a solid foundation in decimals and percentages that will help them in both their academic and practical activities by working through examples and addressing real-world challenges.

Remember that decimals succinctly express fractions, whereas percentages reflect components of a whole in terms of hundredths. The ability to convert between decimals, fractions, and percentages is an essential skill to develop. As a result, with continued practice, you'll become more adept at using decimals and percentages, which will facilitate speedy solutions to a range of mathematical problems.