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To order the numbers from smallest to largest, let’s first convert each number to standard decimal notation.

1. \( 2.002 \times 10^4 = 20,020 \)
2. \( 9.4 \times 10^6 = 9,400,000 \)
3. \( 6.4 \times 10^3 = 6,400 \)
4. \( 6.409 \times 10^3 = 6,409 \)
5. \( 6.46 \times 10^3 = 6,460 \)

Now, arrange them from smallest to largest:

- \( 6.4 \times 10^3 = 6,400 \)
- \( 6.409 \times 10^3 = 6,409 \)
- \( 6.46 \times 10^3 = 6,460 \)
- \( 2.002 \times 10^4 = 20,020 \)
- \( 9.4 \times 10^6 = 9,400,000 \)

Thus, the correct order from smallest to largest is:

1. \( 6.4 \times 10^3 \)
2. \( 6.409 \times 10^3 \)
3. \( 6.46 \times 10^3 \)
4. \( 2.002 \times 10^4 \)
5. \( 9.4 \times 10^6 \)

Would you like more details on this, or do you have any questions?

Here are 5 related questions for further practice:
1. How do you compare two numbers written in scientific notation?
2. What is the process for converting scientific notation into standard form?
3. How would you write \( 3.5 \times 10^5 \) in standard form?
4. What happens when you multiply two numbers in scientific notation?
5. How does scientific notation help in handling very large or small numbers?

**Tip:** When comparing numbers in scientific notation, pay attention to the exponents first. The larger the exponent, the larger the number!

Order the numbers below from smallest (1) to largest (5):
1. 2.002 × 10^4
2. 9.4 × 10^6
3. 6.4 × 10^3
4. 6.409 × 10^3
5. 6.46 × 10^3

Learn how to order numbers written in scientific notation from smallest to largest. This problem involves comparing numbers like 2.002 × 10^4, 9.4 × 10^6, 6.4 × 10^3, 6.409 × 10^3, and 6.46 × 10^3, with a step-by-step solution provided. Suitable for students in Grades 7-9.

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