Math Problem Statement

Solve

Solution

To solve the problem of ordering the numbers from least to greatest, let's convert all the numbers to decimals:

  1. 23\frac{2}{3} = 0.6666...0.6666... (approximately 0.67)
  2. 2.2 (already a decimal)
  3. 4\sqrt{4} = 2 (since the square root of 4 is 2)
  4. 7\sqrt{7} = approximately 2.64575 (since 72.64575\sqrt{7} \approx 2.64575)
  5. 2.3 (already a decimal)

Now, let's list the decimal values:

  • 0.670.67 (approximation of 23\frac{2}{3})
  • 2.02.0 (value of 4\sqrt{4})
  • 2.22.2
  • 2.32.3
  • 2.645752.64575 (approximation of 7\sqrt{7})

Order from least to greatest:

  1. 23\frac{2}{3} (0.67)
  2. 4\sqrt{4} (2.0)
  3. 2.2
  4. 2.3
  5. 7\sqrt{7} (2.64575)

So, the correct order is:

23,4,2.2,2.3,7\frac{2}{3}, \sqrt{4}, 2.2, 2.3, \sqrt{7}

Would you like further details on this solution or any other assistance?


Related questions:

  1. How would you order 34\frac{3}{4}, 1.8, 5\sqrt{5}, 1.9?
  2. Can you express 5\sqrt{5} as a decimal?
  3. What is the decimal approximation for 2\sqrt{2}?
  4. How do you find the square root of a number without a calculator?
  5. What is the decimal form of 58\frac{5}{8}?

Tip: Converting all numbers to a common form, like decimals, helps in easily comparing and ordering them.

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Math Problem Analysis

Mathematical Concepts

Decimal conversions
Ordering numbers

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8