Math Problem Statement

Order the numbers from least to greatest: 3.85 x 10^2, 38,500, 2.8 x 10^3, 3.85 x 10^3, 280,000, 2.8 x 10^4, 2.8, 38.5

Solution

Let's evaluate and arrange the numbers in order from least to greatest. First, we need to convert each number into standard notation.

Here are the numbers provided:

  1. 3.85×102=3853.85 \times 10^2 = 385
  2. 38,50038,500
  3. 2.8×103=28002.8 \times 10^3 = 2800
  4. 3.85×103=38503.85 \times 10^3 = 3850
  5. 280,000280,000
  6. 2.8×104=28,0002.8 \times 10^4 = 28,000
  7. 2.82.8
  8. 38.538.5

Now, let's list them all in standard form:

  1. 385
  2. 38,500
  3. 2,800
  4. 3,850
  5. 280,000
  6. 28,000
  7. 2.8
  8. 38.5

Ordering them from least to greatest:

  • 2.82.8
  • 38.538.5
  • 385385
  • 2,8002,800
  • 3,8503,850
  • 28,00028,000
  • 38,50038,500
  • 280,000280,000

The correct order is:

  1. 2.8
  2. 38.5
  3. 385
  4. 2,800
  5. 3,850
  6. 28,000
  7. 38,500
  8. 280,000

Would you like any further explanation on this?

Here are five related questions to explore:

  1. How do you convert numbers from scientific notation to standard form?
  2. What is the general approach to comparing numbers in different formats?
  3. How can scientific notation be used to simplify comparisons of very large or small numbers?
  4. Why is it important to be able to order numbers from least to greatest in practical scenarios?
  5. How do logarithmic scales relate to scientific notation?

Tip: When comparing numbers in scientific notation, first look at the exponents. If the exponents are equal, then compare the base values.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Standard Form
Ordering Numbers

Formulas

Scientific Notation Conversion: a × 10^n = standard form

Theorems

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Suitable Grade Level

Grades 6-8