Scientific Notation Practice Worksheet with Examples and Problems

Let's solve each problem step by step, following the method shown in the examples. The key idea is to rewrite both numbers so they have the same power of 10, then add or subtract the coefficients. After that, express the result in proper scientific notation (i.e., a number between 1 and 10 multiplied by a power of 10).

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Problem 1:

(2 × 10³) + (5 × 10⁵)

We need the same exponent. Let’s convert both to have 10⁵.

- 2 × 10³ = 0.02 × 10⁵
- So: (0.02 × 10⁵) + (5 × 10⁵) = (0.02 + 5) × 10⁵ = 5.02 × 10⁵

✔ Answer: 5.02 × 10⁵

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Problem 2:

(4 × 10⁸) – (9 × 10⁷)

Convert both to have 10⁸:

- 9 × 10⁷ = 0.9 × 10⁸
- So: (4 × 10⁸) – (0.9 × 10⁸) = (4 – 0.9) × 10⁸ = 3.1 × 10⁸

✔ Answer: 3.1 × 10⁸

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Problem 3:

(8 × 10⁹) – (3 × 10⁷)

Convert both to 10⁹:

- 3 × 10⁷ = 0.03 × 10⁹
- So: (8 × 10⁹) – (0.03 × 10⁹) = (8 – 0.03) × 10⁹ = 7.97 × 10⁹

✔ Answer: 7.97 × 10⁹

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Problem 4:

(5 × 10⁷) + (1 × 10⁶)

Convert both to 10⁷:

- 1 × 10⁶ = 0.1 × 10⁷
- So: (5 × 10⁷) + (0.1 × 10⁷) = (5 + 0.1) × 10⁷ = 5.1 × 10⁷

✔ Answer: 5.1 × 10⁷

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Problem 5:

(4 × 10²) + (7 × 10³)

Convert both to 10³:

- 4 × 10² = 0.4 × 10³
- So: (0.4 × 10³) + (7 × 10³) = (0.4 + 7) × 10³ = 7.4 × 10³

✔ Answer: 7.4 × 10³

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Problem 6:

(9 × 10⁵) – (6 × 10⁴)

Convert both to 10⁵:

- 6 × 10⁴ = 0.6 × 10⁵
- So: (9 × 10⁵) – (0.6 × 10⁵) = (9 – 0.6) × 10⁵ = 8.4 × 10⁵

✔ Answer: 8.4 × 10⁵

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Problem 7:

(1 × 10⁶) – (8 × 10⁴)

Convert both to 10⁶:

- 8 × 10⁴ = 0.08 × 10⁶
- So: (1 × 10⁶) – (0.08 × 10⁶) = (1 – 0.08) × 10⁶ = 0.92 × 10⁶

But this is not in proper scientific notation (0.92 < 1). We fix it:

- 0.92 × 10⁶ = 9.2 × 10⁵

✔ Answer: 9.2 × 10⁵

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Problem 8:

(5 × 10⁹) + (3 × 10⁸)

Convert both to 10⁹:

- 3 × 10⁸ = 0.3 × 10⁹
- So: (5 × 10⁹) + (0.3 × 10⁹) = (5 + 0.3) × 10⁹ = 5.3 × 10⁹

✔ Answer: 5.3 × 10⁹

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | 5.02 × 10⁵ |
| 2) | 3.1 × 10⁸ |
| 3) | 7.97 × 10⁹ |
| 4) | 5.1 × 10⁷ |
| 5) | 7.4 × 10³ |
| 6) | 8.4 × 10⁵ |
| 7) | 9.2 × 10⁵ |
| 8) | 5.3 × 10⁹ |

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🔍 Summary of Strategy:

1. Make exponents the same by adjusting the decimal.
2. Add or subtract the coefficients.
3. Write result in standard scientific notation (coefficient between 1 and 10).

Let me know if you'd like a printable version or explanation for any specific step!