Math Problem Statement

Question content area top Part 1 Reasoning  Which number below comes first when the numbers are listed from least to​ greatest? Explain. Then write the numbers in order from least to greatest. one sixth ​, negative 2​, StartRoot 7 EndRoot​, negative nine halves ​, 1.1 Question content area bottom Part 1 Which number comes first when the numbers are listed from least to​ greatest?

Solution

To determine which number comes first when the numbers are listed from least to greatest, let's convert each of them into decimal form for easier comparison:

  1. One sixth:
    160.1667\frac{1}{6} \approx 0.1667

  2. Negative 2:
    This is already a decimal number: 2.0-2.0

  3. Square root of 7 (7\sqrt{7}):
    72.6458\sqrt{7} \approx 2.6458

  4. Negative nine halves (92-\frac{9}{2}):
    92=4.5-\frac{9}{2} = -4.5

  5. 1.1:
    This is already a decimal number: 1.11.1

Now, let's list these numbers with their approximate decimal forms:

  • One sixth: 0.16670.1667
  • Negative 2: 2.0-2.0
  • 7\sqrt{7}: 2.64582.6458
  • Negative nine halves: 4.5-4.5
  • 1.1: 1.11.1

Finding the Smallest Number

The smallest (most negative) number in the list is negative nine halves (4.5-4.5).

Listing the Numbers in Order

Now, we arrange all the numbers from least to greatest:

  1. 92-\frac{9}{2} (or 4.5-4.5)
  2. 2-2
  3. 16\frac{1}{6} (or approximately 0.16670.1667)
  4. 1.11.1
  5. 7\sqrt{7} (or approximately 2.64582.6458)

Answer

The number that comes first when the numbers are listed from least to greatest is negative nine halves (92-\frac{9}{2}).

Would you like more details or have any questions about this problem?

Here are 5 related questions for practice:

  1. How do you compare fractions with decimals directly?
  2. What is the decimal equivalent of 25\frac{2}{5}?
  3. Which is greater: 0.750.75 or 34\frac{3}{4}?
  4. What is the square root of 55 approximately?
  5. If given three numbers 3-3, 0.50.5, and 10\sqrt{10}, which is the greatest?

Tip: Always convert different forms (fractions, square roots) into decimals to compare them easily.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Number Comparison
Fractions
Square Roots
Negative Numbers

Formulas

Decimal conversion of fractions and square roots

Theorems

Ordering real numbers
Properties of real numbers

Suitable Grade Level

Grades 6-8