Complete The Table. What Number Goes In Box #1?${ \begin{tabular}{|c|c|c|} \hline Fraction & Decimal & Percent \ \hline 5 8 \frac{5}{8} 8 5 ​ & 0.625 & \ \hline 2 & 1.25 & 125 % 125\% 125% \ \hline \end{tabular} }$Your Answer:

In mathematics, fractions, decimals, and percentages are three different ways to represent the same value. Understanding the relationships between these three forms is crucial for solving various mathematical problems. In this article, we will explore how to convert between fractions, decimals, and percentages, and we will use a table to illustrate the conversion process.

The Table: A Tool for Conversion

The table below shows a fraction, its decimal equivalent, and its percentage representation.

Completing the Table: What Number Goes in Box #1?

To complete the table, we need to find the percentage representation of the fraction $\frac{5}{8}$. To do this, we can use the following steps:

1. Convert the fraction to a decimal by dividing the numerator by the denominator: $\frac{5}{8} = 0.625$.
2. Convert the decimal to a percentage by multiplying by 100: $0.625 \times 100 = 62.5\%$.

Therefore, the number that goes in box #1 is 62.5%.

Why is Understanding Fractions, Decimals, and Percentages Important?

Understanding fractions, decimals, and percentages is essential in various mathematical and real-world applications. Here are a few examples:

• Cooking and Recipes: When a recipe calls for a certain amount of an ingredient, it is often represented as a fraction or percentage. For example, a recipe might call for 1/4 cup of sugar or 25% more sugar than the original recipe.
• Finance and Economics: Fractions, decimals, and percentages are used to represent interest rates, inflation rates, and other financial metrics.
• Science and Engineering: Scientists and engineers use fractions, decimals, and percentages to represent measurements, such as the concentration of a solution or the percentage of a material that is used in a product.

Conclusion

In conclusion, understanding the relationships between fractions, decimals, and percentages is crucial for solving various mathematical problems. By using a table to illustrate the conversion process, we can see how to convert between these three forms. We have also seen why understanding fractions, decimals, and percentages is important in various mathematical and real-world applications.

Additional Examples

Here are a few more examples of how to convert between fractions, decimals, and percentages:

• Converting a Fraction to a Decimal: $\frac{3}{4} = 0.75$
• Converting a Decimal to a Percentage: $0.25 \times 100 = 25\%$
• Converting a Percentage to a Decimal: $25\% = 0.25$

Tips and Tricks

Here are a few tips and tricks for working with fractions, decimals, and percentages:

• Use a Calculator: When working with fractions, decimals, and percentages, it is often helpful to use a calculator to ensure accuracy.
• Use a Table or Chart: A table or chart can be a useful tool for illustrating the conversion process and helping to visualize the relationships between fractions, decimals, and percentages.
• Practice, Practice, Practice: The more you practice converting between fractions, decimals, and percentages, the more comfortable you will become with these conversions.

Common Mistakes to Avoid

Here are a few common mistakes to avoid when working with fractions, decimals, and percentages:

• Forgetting to Multiply by 100: When converting a decimal to a percentage, be sure to multiply by 100.
• Forgetting to Divide by the Denominator: When converting a fraction to a decimal, be sure to divide the numerator by the denominator.
• Rounding Errors: When working with fractions, decimals, and percentages, be careful to avoid rounding errors.

Conclusion

In this article, we will answer some of the most frequently asked questions about fractions, decimals, and percentages.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of representing a part of a whole as a ratio of two numbers. For example, 1/2 is a fraction that represents one half of a whole. A decimal, on the other hand, is a way of representing a number as a sum of powers of 10. For example, 0.5 is a decimal that represents one half of a whole.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you can divide the numerator by the denominator. For example, to convert 1/2 to a decimal, you can divide 1 by 2, which equals 0.5.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you can express the decimal as a sum of powers of 10. For example, to convert 0.5 to a fraction, you can express it as 1/2.

Q: What is the difference between a percentage and a decimal?

A: A percentage is a way of representing a part of a whole as a ratio of 100. For example, 25% is a percentage that represents one quarter of a whole. A decimal, on the other hand, is a way of representing a number as a sum of powers of 10. For example, 0.25 is a decimal that represents one quarter of a whole.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, you can divide the percentage by 100. For example, to convert 25% to a decimal, you can divide 25 by 100, which equals 0.25.

Q: How do I convert a decimal to a percentage?

A: To convert a decimal to a percentage, you can multiply the decimal by 100. For example, to convert 0.25 to a percentage, you can multiply 0.25 by 100, which equals 25%.

Q: What is the order of operations for fractions, decimals, and percentages?

A: The order of operations for fractions, decimals, and percentages is as follows:

1. Convert fractions to decimals or percentages.
2. Convert decimals to fractions or percentages.
3. Perform arithmetic operations (addition, subtraction, multiplication, division) on the resulting values.

Q: How do I add or subtract fractions, decimals, and percentages?

A: To add or subtract fractions, decimals, and percentages, you can follow these steps:

1. Convert all values to a common form (e.g., decimals).
2. Perform the arithmetic operation (addition or subtraction).
3. Convert the resulting value back to the original form (e.g., percentage).

Q: How do I multiply or divide fractions, decimals, and percentages?

A: To multiply or divide fractions, decimals, and percentages, you can follow these steps:

1. Convert all values to a common form (e.g., decimals).
2. Perform the arithmetic operation (multiplication or division).
3. Convert the resulting value back to the original form (e.g., percentage).

Q: What are some common mistakes to avoid when working with fractions, decimals, and percentages?

A: Some common mistakes to avoid when working with fractions, decimals, and percentages include:

• Forgetting to multiply by 100 when converting a decimal to a percentage.
• Forgetting to divide by the denominator when converting a fraction to a decimal.
• Rounding errors when performing arithmetic operations.
• Not following the order of operations.

Conclusion

In conclusion, understanding fractions, decimals, and percentages is crucial for solving various mathematical problems. By following the tips and tricks outlined in this article, you can become more comfortable working with these values. Remember to always follow the order of operations and to avoid common mistakes.