Arrange These Numbers From Least To Greatest: 7.52 , 196 25 , 7.855 , 7 17 20 7.52, \frac{196}{25}, 7.855, 7 \frac{17}{20} 7.52 , 25 196 ​ , 7.855 , 7 20 17 ​ Choices: 7.52 □ 7.855 7.52 \, \square \, 7.855 7.52 □ 7.855 7 17 20 7 \frac{17}{20} 7 20 17 ​

Introduction

In mathematics, comparing and arranging numbers in order from least to greatest is a fundamental skill that is essential for solving various mathematical problems. In this article, we will explore how to arrange the given numbers from least to greatest.

The Numbers to Arrange

The numbers to arrange are:

• $7.52$
• $\frac{196}{25}$
• $7.855$
• $7 \frac{17}{20}$

Step 1: Convert the Mixed Number to an Improper Fraction

To compare the numbers, we need to convert the mixed number $7 \frac{17}{20}$ to an improper fraction. To do this, we multiply the whole number part by the denominator and add the numerator.

$7 \frac{17}{20} = \frac{(7 \times 20) + 17}{20} = \frac{140 + 17}{20} = \frac{157}{20}$

Step 2: Convert the Improper Fraction to a Decimal

To compare the numbers, we need to convert the improper fraction $\frac{157}{20}$ to a decimal. To do this, we divide the numerator by the denominator.

$\frac{157}{20} = 7.85$

Step 3: Compare the Numbers

Now that we have converted the mixed number to an improper fraction and then to a decimal, we can compare the numbers.

• $7.52$
• $7.85$
• $7.855$
• $\frac{196}{25}$

To compare the numbers, we need to convert the improper fraction $\frac{196}{25}$ to a decimal. To do this, we divide the numerator by the denominator.

$\frac{196}{25} = 7.84$

Step 4: Arrange the Numbers from Least to Greatest

Now that we have compared the numbers, we can arrange them from least to greatest.

• $7.52$
• $7.84$
• $7.855$
• $7.85$

Conclusion

In conclusion, arranging numbers from least to greatest is a fundamental skill that is essential for solving various mathematical problems. By following the steps outlined in this article, we can compare and arrange numbers in order from least to greatest.

Choosing the Correct Answer

Based on the calculations above, the correct answer is:

• $7.52 \, \square \, 7.855$

This is because $7.52$ is less than $7.855$.

Final Answer

Q: What is the first step in arranging numbers from least to greatest?

A: The first step in arranging numbers from least to greatest is to compare the numbers. To compare numbers, we need to convert them to a common form, such as decimals or fractions.

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

A: To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and add the numerator. For example, to convert $7 \frac{17}{20}$ to an improper fraction, we multiply 7 by 20 and add 17, resulting in $\frac{157}{20}$.

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

A: To convert an improper fraction to a decimal, we divide the numerator by the denominator. For example, to convert $\frac{157}{20}$ to a decimal, we divide 157 by 20, resulting in 7.85.

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

A: A decimal is a way of representing a number using a point to separate the whole number part from the fractional part. A fraction is a way of representing a number as a ratio of two integers. For example, the decimal 7.85 is equivalent to the fraction $\frac{157}{20}$.

Q: How do I compare decimals?

A: To compare decimals, we can compare the whole number parts first, and then the fractional parts. For example, to compare 7.52 and 7.855, we can see that the whole number parts are the same, so we need to compare the fractional parts. Since 0.52 is less than 0.855, 7.52 is less than 7.855.

Q: What is the final step in arranging numbers from least to greatest?

A: The final step in arranging numbers from least to greatest is to arrange the numbers in order from least to greatest. This can be done by comparing the numbers and placing them in order.

Q: Can I use a calculator to arrange numbers from least to greatest?

A: Yes, you can use a calculator to arrange numbers from least to greatest. However, it's always a good idea to understand the steps involved in arranging numbers from least to greatest, so that you can do it manually if needed.

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

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

• Not converting mixed numbers to improper fractions
• Not converting improper fractions to decimals
• Not comparing the whole number parts and fractional parts correctly
• Not arranging the numbers in order from least to greatest

Q: How can I practice arranging numbers from least to greatest?

A: You can practice arranging numbers from least to greatest by working through examples and exercises. You can also try arranging numbers from least to greatest in different contexts, such as in real-world applications or in mathematical problems.

Conclusion

In conclusion, arranging numbers from least to greatest is a fundamental skill that is essential for solving various mathematical problems. By following the steps outlined in this article, you can compare and arrange numbers in order from least to greatest. Remember to practice regularly to build your skills and confidence.