Addition and Subtraction Worksheets with Answer Key - Free Printable

Let's solve each problem step by step, following the rules of addition and subtraction in scientific notation.

🔷 Key Rule:

To add or subtract numbers in scientific notation:
1. The powers of 10 must be the same.
2. If they are different, adjust one or both numbers so that they have the same exponent.
3. Then add or subtract the coefficients.
4. Write the result in proper scientific notation (coefficient between 1 and 10).

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① $ (4.6 \times 10^3) + (8.72 \times 10^3) $

- Same power: $10^3$
- Add coefficients: $4.6 + 8.72 = 13.32$
- Result: $13.32 \times 10^3$
- Convert to proper scientific notation:
$13.32 = 1.332 \times 10^1$, so
$1.332 \times 10^1 \times 10^3 = 1.332 \times 10^4$

✔ Answer: $ \boxed{1.332 \times 10^4} $

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② $ (4.3 \times 10^8) + (2.0 \times 10^6) $

- Different exponents: $10^8$ vs $10^6$
- Convert $2.0 \times 10^6$ to $0.02 \times 10^8$
(since $10^6 = 10^{-2} \times 10^8$, so $2.0 \times 10^6 = 0.02 \times 10^8$)
- Now add: $4.3 + 0.02 = 4.32$
- Result: $4.32 \times 10^8$

✔ Answer: $ \boxed{4.32 \times 10^8} $

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③ $ (1.1 \times 10^5) - (4.3 \times 10^4) $

- Different exponents: $10^5$ vs $10^4$
- Convert $4.3 \times 10^4 = 0.43 \times 10^5$
- Subtract: $1.1 - 0.43 = 0.67$
- Result: $0.67 \times 10^5$
- Convert to proper scientific notation: $0.67 = 6.7 \times 10^{-1}$, so
$6.7 \times 10^{-1} \times 10^5 = 6.7 \times 10^4$

✔ Answer: $ \boxed{6.7 \times 10^4} $

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④ $ (7 \times 10^5) - (5 \times 10^3) $

- Different exponents: $10^5$ vs $10^3$
- Convert $5 \times 10^3 = 0.005 \times 10^5$
- Subtract: $7 - 0.005 = 6.995$
- Result: $6.995 \times 10^5$

✔ Answer: $ \boxed{6.995 \times 10^5} $

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⑤ $ (1.33 \times 10^5) + (4.9 \times 10^4) $

- Different exponents: $10^5$ vs $10^4$
- Convert $4.9 \times 10^4 = 0.49 \times 10^5$
- Add: $1.33 + 0.49 = 1.82$
- Result: $1.82 \times 10^5$

✔ Answer: $ \boxed{1.82 \times 10^5} $

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⑥ $ (8.2 \times 10^2) + (3.41 \times 10^{-1}) $

- Different exponents: $10^2$ vs $10^{-1}$
- Convert $3.41 \times 10^{-1} = 0.00341 \times 10^2$
- Add: $8.2 + 0.00341 = 8.20341$
- Result: $8.20341 \times 10^2$

Now round appropriately? But no rounding is specified, so keep as is.

✔ Answer: $ \boxed{8.20341 \times 10^2} $

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⑦ $ (3.4 \times 10^2) + (4.57 \times 10^3) $

- Different exponents: $10^2$ vs $10^3$
- Convert $3.4 \times 10^2 = 0.34 \times 10^3$
- Add: $0.34 + 4.57 = 4.91$
- Result: $4.91 \times 10^3$

✔ Answer: $ \boxed{4.91 \times 10^3} $

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⑧ $ (3.5 \times 10^{-2}) - (6.6 \times 10^{-3}) $

- Different exponents: $10^{-2}$ vs $10^{-3}$
- Convert $6.6 \times 10^{-3} = 0.66 \times 10^{-2}$
- Subtract: $3.5 - 0.66 = 2.84$
- Result: $2.84 \times 10^{-2}$

✔ Answer: $ \boxed{2.84 \times 10^{-2}} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| ① | $1.332 \times 10^4$ |
| ② | $4.32 \times 10^8$ |
| ③ | $6.7 \times 10^4$ |
| ④ | $6.995 \times 10^5$ |
| ⑤ | $1.82 \times 10^5$ |
| ⑥ | $8.20341 \times 10^2$ |
| ⑦ | $4.91 \times 10^3$ |
| ⑧ | $2.84 \times 10^{-2}$ |

Let me know if you'd like these rounded to significant figures!