Scientific Notation Addition and Subtraction Independent Practice Worksheet.

Let's solve each problem on the Scientific Notation Addition and Subtraction Worksheet step by step.

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🔷 Key Concept:

To add or subtract numbers in scientific notation, you must have the same power of 10. If they don't, convert one or both numbers so they share the same exponent, then perform the operation on the coefficients.

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✔ Problem 1:

9 × 10³ + 2.3 × 10⁴

- Convert both to same exponent. Let’s use 10⁴.
- 9 × 10³ = 0.9 × 10⁴
- Now: 0.9 × 10⁴ + 2.3 × 10⁴ = (0.9 + 2.3) × 10⁴ = 3.2 × 10⁴

✔ Answer: 3.2 × 10⁴

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✔ Problem 2:

15 × 10² + 5.2 × 10⁵

- First, write 15 × 10² in proper scientific notation:
15 × 10² = 1.5 × 10³
- Now: 1.5 × 10³ + 5.2 × 10⁵
- Convert 1.5 × 10³ to 10⁵:
- 1.5 × 10³ = 0.015 × 10⁵
- Add: 0.015 × 10⁵ + 5.2 × 10⁵ = (0.015 + 5.2) × 10⁵ = 5.215 × 10⁵

✔ Answer: 5.215 × 10⁵

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✔ Problem 3:

10 × 10⁴ + 2.8 × 10⁶

- 10 × 10⁴ = 1 × 10⁵
- 2.8 × 10⁶ remains as is
- Convert 1 × 10⁵ → 0.1 × 10⁶
- Add: 0.1 × 10⁶ + 2.8 × 10⁶ = 2.9 × 10⁶

✔ Answer: 2.9 × 10⁶

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✔ Problem 4:

7 × 10³ + 8.6 × 10⁴

- Convert 7 × 10³ to 10⁴:
7 × 10³ = 0.7 × 10⁴
- Add: 0.7 × 10⁴ + 8.6 × 10⁴ = 9.3 × 10⁴

✔ Answer: 9.3 × 10⁴

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✔ Problem 5:

3 × 10⁴ + 14.5 × 10⁵

- Convert 3 × 10⁴ to 10⁵:
3 × 10⁴ = 0.3 × 10⁵
- Add: 0.3 × 10⁵ + 14.5 × 10⁵ = 14.8 × 10⁵
- Convert to proper scientific notation:
14.8 × 10⁵ = 1.48 × 10⁶

✔ Answer: 1.48 × 10⁶

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✔ Problem 6:

8 × 10⁴ − 2.7 × 10²

- Convert 2.7 × 10² to 10⁴:
2.7 × 10² = 0.027 × 10⁴
- Subtract: 8 × 10⁴ − 0.027 × 10⁴ = (8 − 0.027) × 10⁴ = 7.973 × 10⁴

✔ Answer: 7.973 × 10⁴

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✔ Problem 7:

5 × 10³ − 8.9 × 10⁴

- Convert 5 × 10³ to 10⁴:
5 × 10³ = 0.5 × 10⁴
- Subtract: 0.5 × 10⁴ − 8.9 × 10⁴ = (0.5 − 8.9) × 10⁴ = −8.4 × 10⁴

✔ Answer: −8.4 × 10⁴

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✔ Problem 8:

7 × 10³ − 8.20 × 10²

- Convert 8.20 × 10² to 10³:
8.20 × 10² = 0.820 × 10³
- Subtract: 7 × 10³ − 0.820 × 10³ = (7 − 0.820) × 10³ = 6.18 × 10³

✔ Answer: 6.18 × 10³

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✔ Problem 9:

9 × 10⁻² − 5.54 × 10⁴

- Note: These are very different magnitudes.
- 9 × 10⁻² = 0.09
- 5.54 × 10⁴ = 55,400
- So: 0.09 − 55,400 = −55,399.91
- In scientific notation:
−55,399.91 = −5.539991 × 10⁴ ≈ −5.54 × 10⁴ (rounded)

✔ Answer: −5.54 × 10⁴

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✔ Problem 10:

10 × 10² − 7.79 × 10³

- 10 × 10² = 1 × 10³
- Now: 1 × 10³ − 7.79 × 10³ = (1 − 7.79) × 10³ = −6.79 × 10³

✔ Answer: −6.79 × 10³

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 3.2 × 10⁴ |
| 2 | 5.215 × 10⁵ |
| 3 | 2.9 × 10⁶ |
| 4 | 9.3 × 10⁴ |
| 5 | 1.48 × 10⁶ |
| 6 | 7.973 × 10⁴ |
| 7 | −8.4 × 10⁴ |
| 8 | 6.18 × 10³ |
| 9 | −5.54 × 10⁴ |
| 10 | −6.79 × 10³ |

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📌 Tips:

- Always align powers of 10 before adding/subtracting.
- Use decimal shifts carefully.
- Keep track of significant figures if required (though not asked here).

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