Which List Orders The Numbers From Least To Greatest?A. \[$3, -2.5, 1 \frac{1}{2}, -2 \frac{2}{3}, 1.3\$\]B. \[$1.3, 1 \frac{1}{2}, -2.5, -2 \frac{2}{3}, 3\$\]C. \[$-2.5, -2 \frac{2}{3}, 1, 3, 1 \frac{1}{2}, 3\$\]D. \[$-2.5,

by ADMIN 225 views

Introduction

In mathematics, ordering numbers from least to greatest is a fundamental concept that is essential in various mathematical operations and applications. When dealing with a list of numbers, it is crucial to determine the correct order to ensure accuracy and precision in calculations. In this article, we will explore the different options for ordering numbers from least to greatest and identify the correct list.

Understanding the Options

We have four options to consider:

A. ${3, -2.5, 1 \frac{1}{2}, -2 \frac{2}{3}, 1.3\$} B. ${1.3, 1 \frac{1}{2}, -2.5, -2 \frac{2}{3}, 3\$} C. {-2.5, -2 \frac{2}{3}, 1, 3, 1 \frac{1}{2}, 3$}$ D. {-2.5, -2 \frac{2}{3}, 1, 3, 1 \frac{1}{2}, 3$}$

Analyzing the Options

To determine the correct list, we need to compare the numbers in each option and identify the correct order from least to greatest.

Option A

The numbers in option A are: 3, -2.5, 1 1/2, -2 2/3, 1.3

To compare these numbers, we need to convert the mixed numbers to decimal form:

  • 1 1/2 = 1.5
  • -2 2/3 = -2.67

Now, we can compare the numbers in decimal form:

  • -2.67 < -2.5 < 1.3 < 1.5 < 3

Therefore, the correct order from least to greatest for option A is: -2.67, -2.5, 1.3, 1.5, 3.

Option B

The numbers in option B are: 1.3, 1 1/2, -2.5, -2 2/3, 3

To compare these numbers, we need to convert the mixed numbers to decimal form:

  • 1 1/2 = 1.5
  • -2 2/3 = -2.67

Now, we can compare the numbers in decimal form:

  • -2.67 < -2.5 < 1.3 < 1.5 < 3

Therefore, the correct order from least to greatest for option B is: -2.67, -2.5, 1.3, 1.5, 3.

Option C

The numbers in option C are: -2.5, -2 2/3, 1, 3, 1 1/2, 3

To compare these numbers, we need to convert the mixed numbers to decimal form:

  • -2 2/3 = -2.67
  • 1 1/2 = 1.5

Now, we can compare the numbers in decimal form:

  • -2.67 < -2.5 < 1 < 1.5 < 3

Therefore, the correct order from least to greatest for option C is: -2.67, -2.5, 1, 1.5, 3.

Option D

Option D is identical to option C, so the correct order from least to greatest for option D is also: -2.67, -2.5, 1, 1.5, 3.

Conclusion

Based on our analysis, we can conclude that options A, B, C, and D all have the same correct order from least to greatest: -2.67, -2.5, 1.3, 1.5, 3. However, option A and option B have an extra number, 1.3 and 1.5 respectively, which are not present in options C and D. Therefore, the correct list that orders the numbers from least to greatest is option C or option D.

Final Answer

The correct list that orders the numbers from least to greatest is:

{-2.5, -2 \frac{2}{3}, 1, 3, 1 \frac{1}{2}, 3$}$

Q: What is the correct order of the numbers from least to greatest?

A: The correct order of the numbers from least to greatest is: -2.67, -2.5, 1, 1.5, 3.

Q: Why is option C the correct answer?

A: Option C is the correct answer because it correctly orders the numbers from least to greatest. The numbers in option C are: -2.5, -2 2/3, 1, 3, 1 1/2, 3. When we convert the mixed numbers to decimal form, we get: -2.67, -2.5, 1, 1.5, 3. This is the correct order from least to greatest.

Q: What if I have a list of numbers with decimals and fractions? How do I order them from least to greatest?

A: To order a list of numbers with decimals and fractions from least to greatest, you need to convert the fractions to decimal form and then compare the numbers. For example, if you have the list: 1 1/2, 2 3/4, 3, 1/4, 2, you would convert the fractions to decimal form as follows:

  • 1 1/2 = 1.5
  • 2 3/4 = 2.75
  • 1/4 = 0.25

Then, you would compare the numbers in decimal form: 0.25, 1.5, 2, 2.75, 3. This is the correct order from least to greatest.

Q: How do I convert a mixed number to decimal form?

A: To convert a mixed number to decimal form, you need to multiply the whole number part by the denominator and then add the numerator. For example, if you have the mixed number 2 3/4, you would convert it to decimal form as follows:

  • Multiply the whole number part (2) by the denominator (4): 2 x 4 = 8
  • Add the numerator (3): 8 + 3 = 11
  • Divide the result by the denominator (4): 11 ÷ 4 = 2.75

Therefore, the mixed number 2 3/4 is equal to 2.75 in decimal form.

Q: What if I have a list of numbers with negative values? How do I order them from least to greatest?

A: To order a list of numbers with negative values from least to greatest, you need to compare the absolute values of the numbers. For example, if you have the list: -2, -3, 1, 2, 3, you would compare the absolute values of the numbers as follows:

  • |-2| = 2
  • |-3| = 3
  • |1| = 1
  • |2| = 2
  • |3| = 3

Then, you would compare the numbers in absolute value form: 1, 2, 2, 3, 3. This is the correct order from least to greatest.

Q: How do I order a list of numbers with decimals and fractions from least to greatest when there are multiple numbers with the same decimal value?

A: To order a list of numbers with decimals and fractions from least to greatest when there are multiple numbers with the same decimal value, you need to compare the decimal values to the right of the decimal point. For example, if you have the list: 1.5, 1.5, 1.5, 1.5, 1.5, you would compare the decimal values to the right of the decimal point as follows:

  • 1.50
  • 1.50
  • 1.50
  • 1.50
  • 1.50

Since all the numbers have the same decimal value, you would compare the numbers to the right of the decimal point. In this case, there are no numbers to the right of the decimal point, so the numbers are equal.

Q: What if I have a list of numbers with decimals and fractions and I need to order them from greatest to least? How do I do it?

A: To order a list of numbers with decimals and fractions from greatest to least, you need to reverse the order of the numbers from least to greatest. For example, if you have the list: -2.67, -2.5, 1, 1.5, 3, you would reverse the order of the numbers as follows:

  • 3
  • 1.5
  • 1
  • -2.5
  • -2.67

This is the correct order from greatest to least.

Q: How do I order a list of numbers with decimals and fractions when there are multiple numbers with the same decimal value?

A: To order a list of numbers with decimals and fractions when there are multiple numbers with the same decimal value, you need to compare the decimal values to the right of the decimal point. For example, if you have the list: 1.5, 1.5, 1.5, 1.5, 1.5, you would compare the decimal values to the right of the decimal point as follows:

  • 1.50
  • 1.50
  • 1.50
  • 1.50
  • 1.50

Since all the numbers have the same decimal value, you would compare the numbers to the right of the decimal point. In this case, there are no numbers to the right of the decimal point, so the numbers are equal.

Conclusion

Ordering numbers from least to greatest is an essential skill in mathematics. By following the steps outlined in this article, you can easily order a list of numbers with decimals and fractions from least to greatest. Remember to convert fractions to decimal form, compare the decimal values, and reverse the order of the numbers to order them from greatest to least.