Complete The Table.${ \begin{tabular}{|c|c|c|} \hline Fraction & Decimal & Percent \ \hline □ \square □ & 9.4 & □ % \square \% □ % \ 1 1 4 1 \frac{1}{4} 1 4 1 & □ \square □ & □ % \square \% □ % \ \hline \end{tabular} }$(Simplify Your Answer.)

Mar 7, 2025 by ADMIN 246 views

**Converting Between Fractions, Decimals, and Percentages: A Comprehensive Guide**

Introduction

In mathematics, converting between fractions, decimals, and percentages is a fundamental skill that is essential for solving various problems in different fields, such as finance, science, and engineering. In this article, we will provide a step-by-step guide on how to convert between these three types of numbers, using real-world examples and illustrations.

Converting Fractions to Decimals

A fraction is a way of expressing a part of a whole as a ratio of two numbers. For example, the fraction 1/2 represents one half of a whole. To convert a fraction to a decimal, we divide the numerator (the top number) by the denominator (the bottom number).

Example 1: Converting 1/2 to a Decimal

To convert the fraction 1/2 to a decimal, we divide 1 by 2.

1 ÷ 2 = 0.5

Therefore, the decimal equivalent of the fraction 1/2 is 0.5.

Example 2: Converting 3/4 to a Decimal

To convert the fraction 3/4 to a decimal, we divide 3 by 4.

3 ÷ 4 = 0.75

Therefore, the decimal equivalent of the fraction 3/4 is 0.75.

Converting Decimals to Fractions

A decimal is a way of expressing a number as a sum of powers of 10. For example, the decimal 0.5 represents five tenths. To convert a decimal to a fraction, we can use the following steps:

Identify the place value of the last digit in the decimal.
Determine the power of 10 that corresponds to the place value.
Write the decimal as a fraction by using the power of 10 as the denominator.

Example 1: Converting 0.5 to a Fraction

To convert the decimal 0.5 to a fraction, we identify the place value of the last digit, which is tenths. We then determine the power of 10 that corresponds to tenths, which is 10^(-1). Finally, we write the decimal as a fraction by using 10^(-1) as the denominator.

0.5 = 5/10

Therefore, the fraction equivalent of the decimal 0.5 is 5/10.

Example 2: Converting 0.75 to a Fraction

To convert the decimal 0.75 to a fraction, we identify the place value of the last digit, which is hundredths. We then determine the power of 10 that corresponds to hundredths, which is 10^(-2). Finally, we write the decimal as a fraction by using 10^(-2) as the denominator.

0.75 = 75/100

Therefore, the fraction equivalent of the decimal 0.75 is 75/100.

Converting Percentages to Decimals

A percentage is a way of expressing a value as a fraction of 100. For example, the percentage 25% represents 25 out of 100. To convert a percentage to a decimal, we divide the percentage value by 100.

Example 1: Converting 25% to a Decimal

To convert the percentage 25% to a decimal, we divide 25 by 100.

25 ÷ 100 = 0.25

Therefore, the decimal equivalent of the percentage 25% is 0.25.

Example 2: Converting 75% to a Decimal

To convert the percentage 75% to a decimal, we divide 75 by 100.

75 ÷ 100 = 0.75

Therefore, the decimal equivalent of the percentage 75% is 0.75.

Converting Decimals to Percentages

To convert a decimal to a percentage, we multiply the decimal value by 100.

Example 1: Converting 0.5 to a Percentage

To convert the decimal 0.5 to a percentage, we multiply 0.5 by 100.

0.5 × 100 = 50%

Therefore, the percentage equivalent of the decimal 0.5 is 50%.

Example 2: Converting 0.75 to a Percentage

To convert the decimal 0.75 to a percentage, we multiply 0.75 by 100.

0.75 × 100 = 75%

Therefore, the percentage equivalent of the decimal 0.75 is 75%.

Converting Fractions to Percentages

To convert a fraction to a percentage, we divide the numerator by the denominator and then multiply the result by 100.

Example 1: Converting 1/2 to a Percentage

To convert the fraction 1/2 to a percentage, we divide 1 by 2 and then multiply the result by 100.

1 ÷ 2 = 0.5 0.5 × 100 = 50%

Therefore, the percentage equivalent of the fraction 1/2 is 50%.

Example 2: Converting 3/4 to a Percentage

To convert the fraction 3/4 to a percentage, we divide 3 by 4 and then multiply the result by 100.

3 ÷ 4 = 0.75 0.75 × 100 = 75%

Therefore, the percentage equivalent of the fraction 3/4 is 75%.

Conclusion

In conclusion, converting between fractions, decimals, and percentages is a fundamental skill that is essential for solving various problems in different fields. By following the steps outlined in this article, you can easily convert between these three types of numbers. Remember to always identify the place value of the last digit in the decimal, determine the power of 10 that corresponds to the place value, and write the decimal as a fraction by using the power of 10 as the denominator. With practice and patience, you will become proficient in converting between fractions, decimals, and percentages.

Table Completion

Now that we have learned how to convert between fractions, decimals, and percentages, let's complete the table.

Fraction	Decimal	Percent
$\square$	9.4	$\square \%$
$1 \frac{1}{4}$	$\square$	$\square \%$

To complete the table, we need to convert the fraction $1 \frac{1}{4}$ to a decimal and a percentage.

Converting $1 \frac{1}{4}$ to a Decimal

To convert the fraction $1 \frac{1}{4}$ to a decimal, we can convert the mixed number to an improper fraction and then divide the numerator by the denominator.

$1 \frac{1}{4} = \frac{5}{4}$ $\frac{5}{4} = 1.25$

Therefore, the decimal equivalent of the fraction $1 \frac{1}{4}$ is 1.25.

Converting $1 \frac{1}{4}$ to a Percentage

To convert the fraction $1 \frac{1}{4}$ to a percentage, we can divide the numerator by the denominator and then multiply the result by 100.

$\frac{5}{4} = 1.25$ $1.25 × 100 = 125\%$

Therefore, the percentage equivalent of the fraction $1 \frac{1}{4}$ is 125%.

Now that we have completed the table, we can see that the decimal equivalent of the fraction $1 \frac{1}{4}$ is 1.25 and the percentage equivalent is 125%.

Fraction	Decimal	Percent
$\square$	9.4	$\square \%$
$1 \frac{1}{4}$	1.25	125%

To complete the table, we need to convert the decimal 9.4 to a percentage.

Converting 9.4 to a Percentage

To convert the decimal 9.4 to a percentage, we can multiply the decimal value by 100.

9.4 × 100 = 940%

Therefore, the percentage equivalent of the decimal 9.4 is 940%.

Now that we have completed the table, we can see that the decimal equivalent of the fraction $\square$ is 9.4 and the percentage equivalent is 940%.

Fraction	Decimal	Percent
1/2	9.4	940%
$1 \frac{1}{4}$	1.25	125%

Therefore, the completed table is:

Fraction	Decimal	Percent
1/2	9.4	940%
$1 \frac{1}{4}$	1.25	125%

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

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. A decimal is a way of expressing a number as a sum of powers of 10. A percentage is a way of expressing 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 1/2 to a decimal, you 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 use the following steps:

Identify the place value of the last digit in the decimal.
Determine the power of 10 that corresponds to the place value.
Write the decimal as a fraction by using the power of 10 as the denominator.

For example, to convert the decimal 0.5 to a fraction, you identify the place value of the last digit, which is tenths. You then determine the power of 10 that corresponds to tenths, which is 10^(-1). Finally, you write the decimal as a fraction by using 10^(-1) as the denominator.

0.5 = 5/10

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

A: To convert a percentage to a decimal, you divide the percentage value by 100. For example, to convert the percentage 25% to a decimal, you 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 multiply the decimal value by 100. For example, to convert the decimal 0.5 to a percentage, you multiply 0.5 by 100, which equals 50%.

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

A: To convert a fraction to a percentage, you divide the numerator by the denominator and then multiply the result by 100. For example, to convert the fraction 1/2 to a percentage, you divide 1 by 2 and then multiply the result by 100, which equals 50%.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a way of expressing a number as a combination of a whole number and a fraction. An improper fraction is a way of expressing a number as a fraction where the numerator is greater than the denominator.

For example, the mixed number 2 1/2 is equal to the improper fraction 5/2.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and then add the numerator. You then write the result as a fraction with the denominator.

For example, to convert the mixed number 2 1/2 to an improper fraction, you multiply 2 by 2 and then add 1, which equals 5. You then write the result as a fraction with the denominator.

2 1/2 = 5/2

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, you divide the numerator by the denominator and then write the result as a combination of a whole number and a fraction.

For example, to convert the improper fraction 5/2 to a mixed number, you divide 5 by 2, which equals 2 with a remainder of 1. You then write the result as a combination of a whole number and a fraction.

5/2 = 2 1/2

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

A: Some common mistakes to avoid when converting between fractions, decimals, and percentages include:

Forgetting to divide the numerator by the denominator when converting a fraction to a decimal.
Forgetting to multiply the decimal value by 100 when converting a decimal to a percentage.
Forgetting to divide the percentage value by 100 when converting a percentage to a decimal.
Forgetting to multiply the numerator by the denominator and then add the numerator when converting a mixed number to an improper fraction.
Forgetting to divide the numerator by the denominator and then write the result as a combination of a whole number and a fraction when converting an improper fraction to a mixed number.

By avoiding these common mistakes, you can ensure that your conversions are accurate and reliable.