Math Problem Statement

Dalen has a set of real numbers that needs to be ordered from least to greatest.

Which of the following shows the order Dalen should place his numbers? A.227, 200%, 53, 2–√

B.2–√, 53, 200%, 227

C.53, 200%, 227, 2–√

D.2–√, 53, 227, 200%

Solution

To determine the correct order from least to greatest, let's evaluate each number:

  1. 227227: This is already a number, and it equals 227227.

  2. 200%200\%: This means 200%200\% of something, which is 200%×1=2200\% \times 1 = 2.

  3. 5353: This is already a number, and it equals 5353.

  4. 2\sqrt{2}: The square root of 2 is approximately 1.4141.414.

Now, let's list all the numbers:

  • 21.414\sqrt{2} \approx 1.414
  • 22
  • 5353
  • 227227

The correct order from least to greatest is:

  • 21.414\sqrt{2} \approx 1.414
  • 22
  • 5353
  • 227227

This corresponds to Option B: 2,53,200%,227\sqrt{2}, 53, 200\%, 227.

Would you like further details or have any questions?

Here are 5 related questions to think about:

  1. How do you convert percentages to decimals?
  2. What is the decimal approximation of 3\sqrt{3}?
  3. How can you compare irrational numbers with rational numbers?
  4. What are some common square roots to memorize for quicker calculations?
  5. How do percentages greater than 100% compare to whole numbers?

Tip: When comparing different types of numbers, it's often helpful to convert all numbers to decimals for easier comparison.

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Math Problem Analysis

Mathematical Concepts

Ordering real numbers
Percentages
Square roots

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9