Converting the Numbers to Decimal Form

Oct 13, 2025 by miodeya.com 129 views

Which Set of Numbers is Correctly Ordered from Least to Greatest?

Understanding the Options

When presented with a set of numbers, it's essential to understand the concept of ordering them from least to greatest. This involves comparing each number to determine its relative size. In this case, we have four options, each containing three numbers: A, B, C, and D. Our task is to identify the correct order from least to greatest.

Analyzing the Numbers

To determine the correct order, we need to analyze each number individually. Let's start by converting the numbers to a common format for easier comparison.

Option A: $\frac{24 \pi}{5}, \frac{63}{4}, 15.758$
Option B: $\frac{24 \pi}{5}, 15.758, \frac{63}{4}$
Option C: $15.758, \frac{63}{4}, \frac{24 \pi}{5}$
Option D: $\frac{63}{4}, \frac{24 \pi}{5}, 15.758$

Converting the Numbers to Decimal Form

To make the comparison easier, let's convert the numbers to decimal form.

$\frac{24 \pi}{5}$ ≈ 15.09
$\frac{63}{4}$ = 15.75
15.758 ≈ 15.76

Comparing the Numbers

Now that we have the numbers in decimal form, let's compare them to determine the correct order from least to greatest.

15.09 (≈ $\frac{24 \pi}{5}$ ) is less than 15.75 (≈ $\frac{63}{4}$ )
15.75 (≈ $\frac{63}{4}$ ) is less than 15.76 (≈ 15.758)
15.09 (≈ $\frac{24 \pi}{5}$ ) is less than 15.76 (≈ 15.758)

Determining the Correct Order

Based on the comparison, we can determine the correct order from least to greatest.

The correct order is: $\frac{24 \pi}{5}, \frac{63}{4}, 15.758$

Conclusion

In conclusion, the correct set of numbers ordered from least to greatest is:

$\frac{24 \pi}{5}, \frac{63}{4}, 15.758$

This is the correct order, as it follows the logical sequence of numbers from least to greatest.

Additional Tips and Tricks

When presented with a set of numbers, it's essential to understand the concept of ordering them from least to greatest. This involves comparing each number to determine its relative size. By converting the numbers to a common format and comparing them, we can determine the correct order.

Common Mistakes to Avoid

When ordering numbers from least to greatest, it's essential to avoid common mistakes, such as:

Comparing numbers without converting them to a common format
Failing to consider the relative size of each number
Not following the logical sequence of numbers from least to greatest

Real-World Applications

Understanding how to order numbers from least to greatest has real-world applications in various fields, such as:

Mathematics: Ordering numbers is a fundamental concept in mathematics, and it's essential for solving problems and making calculations.
Science: In science, ordering numbers is crucial for understanding and analyzing data.
Finance: In finance, ordering numbers is essential for making informed decisions and managing risk.

Conclusion

In conclusion, ordering numbers from least to greatest is a fundamental concept in mathematics and has real-world applications in various fields. By understanding how to compare numbers and determine their relative size, we can make informed decisions and solve problems effectively.
Frequently Asked Questions (FAQs) About Ordering Numbers from Least to Greatest

Q: What is the correct order of the numbers $\frac{24 \pi}{5}, \frac{63}{4}, 15.758$ ?

A: The correct order is $\frac{24 \pi}{5}, \frac{63}{4}, 15.758$ . This is because $\frac{24 \pi}{5}$ is approximately 15.09, which is less than $\frac{63}{4}$ , which is approximately 15.75. 15.758 is greater than both of these numbers.

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 $\frac{24 \pi}{5}$ to a decimal, you can divide 24 by 5 and then multiply the result by $\pi$ . This will give you an approximate decimal value.

Q: What is the difference between $\frac{63}{4}$ and 15.758?

A: $\frac{63}{4}$ is approximately 15.75, while 15.758 is greater than this value. This means that $\frac{63}{4}$ is less than 15.758.

Q: Can you explain why $\frac{24 \pi}{5}$ is less than $\frac{63}{4}$ ?

A: Yes, $\frac{24 \pi}{5}$ is less than $\frac{63}{4}$ because $\pi$ is approximately 3.14. When you multiply 24 by 3.14, you get 75.36. Dividing this value by 5 gives you approximately 15.09, which is less than 15.75.

Q: How do I determine the correct order of numbers when they are in decimal form?

A: To determine the correct order of numbers when they are in decimal form, you can compare the decimal values. The number with the smallest decimal value is the least, while the number with the largest decimal value is the greatest.

Q: Can you provide an example of how to order numbers from least to greatest?

A: Yes, let's say we have the numbers 12.5, 15.2, and 18.7. To order these numbers from least to greatest, we can compare their decimal values. 12.5 is less than 15.2, which is less than 18.7. Therefore, the correct order is 12.5, 15.2, 18.7.

Q: What is the importance of ordering numbers from least to greatest?

A: Ordering numbers from least to greatest is important because it allows us to compare and analyze data effectively. It is also essential for making informed decisions and solving problems in various fields, such as mathematics, science, and finance.

Q: Can you explain why ordering numbers from least to greatest is a fundamental concept in mathematics?

A: Yes, ordering numbers from least to greatest is a fundamental concept in mathematics because it allows us to compare and analyze data effectively. It is also essential for making calculations and solving problems in various mathematical operations, such as addition, subtraction, multiplication, and division.

Q: How do I apply the concept of ordering numbers from least to greatest in real-world situations?

A: To apply the concept of ordering numbers from least to greatest in real-world situations, you can use it to compare and analyze data in various fields, such as science, finance, and business. For example, you can use it to compare the prices of different products, the heights of different buildings, or the scores of different athletes.

Q: Can you provide a real-world example of how ordering numbers from least to greatest is used in science?

A: Yes, let's say we have a set of data on the heights of different plants. To analyze this data, we can order the heights from least to greatest. This will allow us to compare the heights of different plants and make informed decisions about which plants to study further.

Q: What are some common mistakes to avoid when ordering numbers from least to greatest?

A: Some common mistakes to avoid when ordering numbers from least to greatest include:

Comparing numbers without converting them to a common format
Failing to consider the relative size of each number
Not following the logical sequence of numbers from least to greatest

Q: Can you explain why it is essential to avoid these common mistakes?

A: Yes, it is essential to avoid these common mistakes because they can lead to incorrect conclusions and poor decision-making. By avoiding these mistakes, you can ensure that you are ordering numbers from least to greatest accurately and effectively.