Math Problem Statement

Put the following numbers in order from least to greatest: 12,300; 2.13 × 10⁻⁵; 4.56 × 10⁻¹; 1.23 × 10².

Solution

The question asks to arrange the following numbers in order from least to greatest. Let's first convert them into standard notation:

  1. 2.13×105=0.00002132.13 \times 10^{-5} = 0.0000213
  2. 4.56×101=0.4564.56 \times 10^{-1} = 0.456
  3. 1.23×102=1231.23 \times 10^2 = 123
  4. 12,30012,300 (already in standard form)

Now, we can arrange them:

  • 0.00002130.0000213 (smallest)
  • 0.4560.456
  • 123123
  • 12,30012,300 (largest)

So, the numbers in order from least to greatest are: 2.13×105,4.56×101,1.23×102,12,300.2.13 \times 10^{-5}, 4.56 \times 10^{-1}, 1.23 \times 10^2, 12,300.

Would you like further explanation or have any questions?

Here are 5 related questions:

  1. What is scientific notation and why is it useful?
  2. How do you convert scientific notation to standard notation?
  3. How would you multiply two numbers in scientific notation?
  4. Can you explain the rules for adding and subtracting numbers in scientific notation?
  5. What is the relationship between powers of 10 and the decimal point?

Tip: When comparing numbers in scientific notation, focus on the exponent first. The higher the exponent, the larger the number.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Ordering Numbers

Formulas

Standard Form Conversion

Theorems

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Suitable Grade Level

Grades 6-8