Complete The Chart. \[ \begin{tabular}{|c|c|c|} \hline Fraction & Decimal & Percent \\ \hline \frac{6}{10}$ & & \ \hline 67 100 \frac{67}{100} 100 67 & & \ \hline 2 20 \frac{2}{20} 20 2 & & \ \hline 3 5 \frac{3}{5} 5 3 & &
Introduction
In mathematics, fractions, decimals, and percentages are three different ways to represent the same value. Understanding how to convert between these forms is essential for solving problems in various fields, including finance, science, and engineering. In this article, we will explore the process of converting fractions to decimals and percentages, and provide examples to illustrate the concepts.
Converting Fractions to Decimals
A fraction is a way of representing a part of a whole as a ratio of two numbers. The top number, or numerator, represents the number of equal parts, while the bottom number, or denominator, represents the total number of parts. To convert a fraction to a decimal, we divide the numerator by the denominator.
Example 1: Converting 6/10 to a Decimal
To convert the fraction 6/10 to a decimal, we divide the numerator (6) by the denominator (10).
6 ÷ 10 = 0.6
Therefore, the decimal equivalent of 6/10 is 0.6.
Example 2: Converting 67/100 to a Decimal
To convert the fraction 67/100 to a decimal, we divide the numerator (67) by the denominator (100).
67 ÷ 100 = 0.67
Therefore, the decimal equivalent of 67/100 is 0.67.
Example 3: Converting 2/20 to a Decimal
To convert the fraction 2/20 to a decimal, we divide the numerator (2) by the denominator (20).
2 ÷ 20 = 0.1
Therefore, the decimal equivalent of 2/20 is 0.1.
Example 4: Converting 3/5 to a Decimal
To convert the fraction 3/5 to a decimal, we divide the numerator (3) by the denominator (5).
3 ÷ 5 = 0.6
Therefore, the decimal equivalent of 3/5 is 0.6.
Converting Decimals to Percentages
A percentage is a way of representing a value as a fraction of 100. To convert a decimal to a percentage, we multiply the decimal by 100.
Example 1: Converting 0.6 to a Percentage
To convert the decimal 0.6 to a percentage, we multiply it by 100.
0.6 × 100 = 60%
Therefore, the percentage equivalent of 0.6 is 60%.
Example 2: Converting 0.67 to a Percentage
To convert the decimal 0.67 to a percentage, we multiply it by 100.
0.67 × 100 = 67%
Therefore, the percentage equivalent of 0.67 is 67%.
Example 3: Converting 0.1 to a Percentage
To convert the decimal 0.1 to a percentage, we multiply it by 100.
0.1 × 100 = 10%
Therefore, the percentage equivalent of 0.1 is 10%.
Example 4: Converting 0.6 to a Percentage
To convert the decimal 0.6 to a percentage, we multiply it by 100.
0.6 × 100 = 60%
Therefore, the percentage equivalent of 0.6 is 60%.
Converting Percentages to Decimals
To convert a percentage to a decimal, we divide the percentage by 100.
Example 1: Converting 60% to a Decimal
To convert the percentage 60% to a decimal, we divide it by 100.
60 ÷ 100 = 0.6
Therefore, the decimal equivalent of 60% is 0.6.
Example 2: Converting 67% to a Decimal
To convert the percentage 67% to a decimal, we divide it by 100.
67 ÷ 100 = 0.67
Therefore, the decimal equivalent of 67% is 0.67.
Example 3: Converting 10% to a Decimal
To convert the percentage 10% to a decimal, we divide it by 100.
10 ÷ 100 = 0.1
Therefore, the decimal equivalent of 10% is 0.1.
Example 4: Converting 60% to a Decimal
To convert the percentage 60% to a decimal, we divide it by 100.
60 ÷ 100 = 0.6
Therefore, the decimal equivalent of 60% is 0.6.
Conclusion
Q: What is the difference between a fraction, a decimal, and a percentage?
A: A fraction is a way of representing a part of a whole as a ratio of two numbers. A decimal is a way of representing a value as a number with a point separating the whole number part from the fractional part. A percentage is a way of representing a value as a fraction of 100.
Q: How do I convert a fraction to a decimal?
A: To convert a fraction to a decimal, you divide the numerator (the top number) by the denominator (the bottom number). For example, to convert the fraction 3/4 to a decimal, you would divide 3 by 4, which equals 0.75.
Q: How do I convert a decimal to a percentage?
A: To convert a decimal to a percentage, you multiply the decimal by 100. For example, to convert the decimal 0.75 to a percentage, you would multiply 0.75 by 100, which equals 75%.
Q: How do I convert a percentage to a decimal?
A: To convert a percentage to a decimal, you divide the percentage by 100. For example, to convert the percentage 75% to a decimal, you would divide 75 by 100, which equals 0.75.
Q: What is the easiest way to convert fractions to decimals and percentages?
A: The easiest way to convert fractions to decimals and percentages is to use a calculator or a computer program. However, if you don't have access to a calculator or computer program, you can use the following steps:
- To convert a fraction to a decimal, divide the numerator by the denominator.
- To convert a decimal to a percentage, multiply the decimal by 100.
- To convert a percentage to a decimal, divide the percentage by 100.
Q: Can I convert a mixed number to a decimal or percentage?
A: Yes, you can convert a mixed number to a decimal or percentage. To convert a mixed number to a decimal, you need to convert the whole number part and the fractional part separately. For example, to convert the mixed number 2 3/4 to a decimal, you would convert the whole number part (2) to a decimal (2.0) and the fractional part (3/4) to a decimal (0.75), and then add the two decimals together (2.0 + 0.75 = 2.75).
Q: Can I convert a decimal or percentage to a fraction?
A: Yes, you can convert a decimal or percentage to a fraction. To convert a decimal to a fraction, you need to express the decimal as a ratio of two numbers. For example, to convert the decimal 0.75 to a fraction, you would express it as 75/100, which can be simplified to 3/4. To convert a percentage to a fraction, you need to express the percentage as a ratio of two numbers. For example, to convert the percentage 75% to a fraction, you would express it as 75/100, which can be simplified to 3/4.
Q: Why is it important to be able to convert fractions to decimals and percentages?
A: It is important to be able to convert fractions to decimals and percentages because it allows you to work with different types of numbers and to solve problems in various fields, such as finance, science, and engineering. For example, in finance, you may need to convert a percentage to a decimal to calculate interest rates or investment returns. In science, you may need to convert a fraction to a decimal to calculate measurements or concentrations. In engineering, you may need to convert a percentage to a fraction to calculate material properties or structural loads.