Math Problem Statement

Write these numbers in order, starting with the largest: 6.1 × 10^1, 2.03 × 10^3, 8.79 × 10^-2, 2 × 10^2.

Solution

Let's start by converting all the numbers to their standard decimal form to compare them easily:

  1. 6.1×1016.1 \times 10^1 = 6161
  2. 2.03×1032.03 \times 10^3 = 20302030
  3. 8.79×1028.79 \times 10^{-2} = 0.08790.0879
  4. 2×1022 \times 10^2 = 200200

Now, let's arrange these values from the largest to the smallest:

  • 2.03×1032.03 \times 10^3 (2030)
  • 2×1022 \times 10^2 (200)
  • 6.1×1016.1 \times 10^1 (61)
  • 8.79×1028.79 \times 10^{-2} (0.0879)

Thus, the order from largest to smallest is:

B, D, A, C

Would you like more details or explanations on any step?

Here are five related questions to expand your understanding:

  1. How do you convert scientific notation into standard decimal form?
  2. What are the common powers of 10 and how do they scale numbers?
  3. How would the process change if one of the numbers had a negative exponent?
  4. Can you explain the difference between positive and negative powers of 10?
  5. How can scientific notation help simplify comparisons between very large or small numbers?

Tip: To compare numbers in scientific notation, focus on the exponent first; the number with the higher exponent will usually be larger.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponents
Number Comparison

Formulas

Standard form of scientific notation: a × 10^n
Decimal conversion of scientific notation

Theorems

Exponent rules for multiplying and comparing powers of 10

Suitable Grade Level

Grades 6-8