Math Problem Statement

Order the following scientific notation values from smallest to largest: 1. 2.5 × 10⁻⁶ 2. 1.7 × 10⁻⁶ 3. 5.3 × 10⁻⁵ 4. 2.5 × 10⁻⁵ 5. 5.3 × 10⁻⁴

Solution

From the image, the problem asks to order the given scientific notations from smallest to largest. Let's analyze the values:

Given values:

  1. 2.51062.5 \cdot 10^{-6}
  2. 1.71061.7 \cdot 10^{-6}
  3. 5.31055.3 \cdot 10^{-5}
  4. 2.51052.5 \cdot 10^{-5}
  5. 5.31045.3 \cdot 10^{-4}

Step-by-step:

  1. Compare the powers of 10. A smaller exponent corresponds to a smaller value (e.g., 106<105<10410^{-6} < 10^{-5} < 10^{-4}).
  2. Within the same power of 10, compare the coefficients (e.g., for 10610^{-6}, 1.7<2.51.7 < 2.5).

Ordered values:

  • 1.71061.7 \cdot 10^{-6} (smallest)
  • 2.51062.5 \cdot 10^{-6}
  • 2.51052.5 \cdot 10^{-5}
  • 5.31055.3 \cdot 10^{-5}
  • 5.31045.3 \cdot 10^{-4} (largest)

Final answer:

  1. 1.71061.7 \cdot 10^{-6}
  2. 2.51062.5 \cdot 10^{-6}
  3. 2.51052.5 \cdot 10^{-5}
  4. 5.31055.3 \cdot 10^{-5}
  5. 5.31045.3 \cdot 10^{-4}

Would you like further explanation on scientific notation or help with another topic?


Here are some follow-up questions:

  1. How is the placement of numbers in scientific notation affected by the exponent?
  2. Why does the coefficient matter when the exponent is the same?
  3. What is a real-world application of ordering numbers in scientific notation?
  4. Can you explain why 10610^{-6} is smaller than 10510^{-5}?
  5. How do you multiply and divide numbers in scientific notation?

Tip: Always start by comparing exponents when ordering numbers in scientific notation.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Ordering Numbers
Exponents

Formulas

Scientific Notation Comparison: Compare exponents first, then coefficients

Theorems

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Suitable Grade Level

Grades 6-8