Free Adding and Subtracting Scientific Notation Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Scientific Notation: Addition and Subtraction – Independent Practice Worksheet". The task is to perform addition and subtraction operations with numbers written in scientific notation.

Here's the list of problems from the worksheet:

1. $ 2 \times 10^5 + 2.3 \times 10^4 $
2. $ 7.1 \times 10^3 - 6.2 \times 10^3 $
3. $ 3.2 \times 10^8 - 2.9 \times 10^7 $
4. $ 7 \times 10^5 + 8.4 \times 10^4 $
5. $ 1.1 \times 10^4 + 14.5 \times 10^3 $
6. $ 3 \times 10^9 - 2.7 \times 10^8 $
7. $ 5.4 \times 10^6 - 8.2 \times 10^5 $
8. $ 7 \times 10^9 - 8.2 \times 10^8 $
9. $ 2 \times 10^9 - 5.2 \times 10^8 $
10. $ 11 \times 10^2 - 7.9 \times 10^2 $

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🔧 Key Rule for Adding/Subtracting Scientific Notation:

To add or subtract numbers in scientific notation, they must have the same exponent (power of 10). If not, convert one or both numbers so that they have the same exponent, then perform the operation on the coefficients.

Let’s solve each problem step by step.

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✔ Problem 1:

$ 2 \times 10^5 + 2.3 \times 10^4 $

Convert $ 2.3 \times 10^4 $ to match $ 10^5 $:
$ 2.3 \times 10^4 = 0.23 \times 10^5 $

Now add:
$ 2 \times 10^5 + 0.23 \times 10^5 = (2 + 0.23) \times 10^5 = 2.23 \times 10^5 $

✔ Answer: $ 2.23 \times 10^5 $

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✔ Problem 2:

$ 7.1 \times 10^3 - 6.2 \times 10^3 $

Same exponent:
$ (7.1 - 6.2) \times 10^3 = 0.9 \times 10^3 $

Convert to proper scientific notation:
$ 0.9 \times 10^3 = 9 \times 10^2 $

✔ Answer: $ 9 \times 10^2 $

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✔ Problem 3:

$ 3.2 \times 10^8 - 2.9 \times 10^7 $

Convert $ 2.9 \times 10^7 $ to $ 10^8 $:
$ 2.9 \times 10^7 = 0.29 \times 10^8 $

Now subtract:
$ 3.2 \times 10^8 - 0.29 \times 10^8 = (3.2 - 0.29) \times 10^8 = 2.91 \times 10^8 $

✔ Answer: $ 2.91 \times 10^8 $

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✔ Problem 4:

$ 7 \times 10^5 + 8.4 \times 10^4 $

Convert $ 8.4 \times 10^4 $ to $ 10^5 $:
$ 8.4 \times 10^4 = 0.84 \times 10^5 $

Add:
$ 7 \times 10^5 + 0.84 \times 10^5 = 7.84 \times 10^5 $

✔ Answer: $ 7.84 \times 10^5 $

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✔ Problem 5:

$ 1.1 \times 10^4 + 14.5 \times 10^3 $

Convert $ 14.5 \times 10^3 $ to $ 10^4 $:
$ 14.5 \times 10^3 = 1.45 \times 10^4 $

Add:
$ 1.1 \times 10^4 + 1.45 \times 10^4 = (1.1 + 1.45) \times 10^4 = 2.55 \times 10^4 $

✔ Answer: $ 2.55 \times 10^4 $

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✔ Problem 6:

$ 3 \times 10^9 - 2.7 \times 10^8 $

Convert $ 2.7 \times 10^8 $ to $ 10^9 $:
$ 2.7 \times 10^8 = 0.27 \times 10^9 $

Subtract:
$ 3 \times 10^9 - 0.27 \times 10^9 = (3 - 0.27) \times 10^9 = 2.73 \times 10^9 $

✔ Answer: $ 2.73 \times 10^9 $

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✔ Problem 7:

$ 5.4 \times 10^6 - 8.2 \times 10^5 $

Convert $ 8.2 \times 10^5 $ to $ 10^6 $:
$ 8.2 \times 10^5 = 0.82 \times 10^6 $

Subtract:
$ 5.4 \times 10^6 - 0.82 \times 10^6 = (5.4 - 0.82) \times 10^6 = 4.58 \times 10^6 $

✔ Answer: $ 4.58 \times 10^6 $

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✔ Problem 8:

$ 7 \times 10^9 - 8.2 \times 10^8 $

Convert $ 8.2 \times 10^8 $ to $ 10^9 $:
$ 8.2 \times 10^8 = 0.82 \times 10^9 $

Subtract:
$ 7 \times 10^9 - 0.82 \times 10^9 = (7 - 0.82) \times 10^9 = 6.18 \times 10^9 $

✔ Answer: $ 6.18 \times 10^9 $

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✔ Problem 9:

$ 2 \times 10^9 - 5.2 \times 10^8 $

Convert $ 5.2 \times 10^8 $ to $ 10^9 $:
$ 5.2 \times 10^8 = 0.52 \times 10^9 $

Subtract:
$ 2 \times 10^9 - 0.52 \times 10^9 = (2 - 0.52) \times 10^9 = 1.48 \times 10^9 $

✔ Answer: $ 1.48 \times 10^9 $

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✔ Problem 10:

$ 11 \times 10^2 - 7.9 \times 10^2 $

Same exponent:
$ (11 - 7.9) \times 10^2 = 3.1 \times 10^2 $

✔ Answer: $ 3.1 \times 10^2 $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ 2.23 \times 10^5 $ |
| 2 | $ 9 \times 10^2 $ |
| 3 | $ 2.91 \times 10^8 $ |
| 4 | $ 7.84 \times 10^5 $ |
| 5 | $ 2.55 \times 10^4 $ |
| 6 | $ 2.73 \times 10^9 $ |
| 7 | $ 4.58 \times 10^6 $ |
| 8 | $ 6.18 \times 10^9 $ |
| 9 | $ 1.48 \times 10^9 $ |
| 10 | $ 3.1 \times 10^2 $ |

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📌 Tips for Success:

- Always make sure the powers of 10 are the same before adding/subtracting.
- Adjust the smaller number by moving the decimal point and changing the exponent accordingly.
- After calculating, ensure your answer is in proper scientific notation (coefficient between 1 and 10).

Let me know if you'd like this as a downloadable PDF or want explanations in a different format!