Math Problem Statement

Which list shows the numbers in order from least to greatest? The numbers provided are -4/3, -0.43, √3, and 5/2.

Solution

To solve this problem, we need to order the given numbers from least to greatest. The numbers are:

  • 43-\frac{4}{3}
  • 0.43-0.43
  • 3\sqrt{3}
  • 52\frac{5}{2}

Step 1: Converting all numbers to decimal form for easy comparison.

  1. 431.33-\frac{4}{3} \approx -1.33
  2. 0.43-0.43 (already in decimal form)
  3. 31.732\sqrt{3} \approx 1.732
  4. 52=2.5\frac{5}{2} = 2.5

Step 2: Ordering these values.

Now, comparing the numbers in decimal form:

  • 1.33-1.33
  • 0.43-0.43
  • 1.7321.732
  • 2.52.5

From least to greatest: 1.33,0.43,1.732,2.5-1.33, -0.43, 1.732, 2.5

Step 3: Match with the options provided.

  • Option A lists the numbers in the correct order:
    43,0.43,3,52-\frac{4}{3}, -0.43, \sqrt{3}, \frac{5}{2}.

Thus, the correct answer is A.


Would you like more details on any step? Here are 5 related questions for further exploration:

  1. How can you convert fractions to decimals?
  2. What is the significance of ordering rational and irrational numbers?
  3. Why is 31.732\sqrt{3} \approx 1.732?
  4. What are other methods to compare numbers without converting them?
  5. How do you handle the order of negative numbers when comparing?

Tip: When comparing fractions and irrational numbers, converting them into decimals can make it easier to determine the correct order.

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Math Problem Analysis

Mathematical Concepts

Comparing Numbers
Fractions
Square Roots
Ordering Rational and Irrational Numbers

Formulas

Fraction to Decimal Conversion
Square Root Approximation

Theorems

Properties of Rational and Irrational Numbers
Ordering Negative and Positive Numbers

Suitable Grade Level

Grades 6-8