Adding And Subtracting In Scientific Notation Worksheet, Practice ... - Free Printable

Let's solve each problem step by step. The goal is to add or subtract numbers in scientific notation. To do this, we must ensure that the powers of 10 are the same before performing the operation on the coefficients.

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🔷 Rule Reminder:

To add or subtract numbers in scientific notation:
1. Make sure both numbers have the same exponent (power of 10).
2. If they don’t, adjust one or both numbers so they do.
3. Add or subtract the coefficients.
4. Keep the common power of 10.
5. Write the result in proper scientific notation (coefficient between 1 and 10).

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✔ Problem 1:

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

- Same exponent: $10^9$
- Subtract coefficients: $9 - 2 = 7$
- Result: $7 \times 10^9$

✔ Answer: $ \boxed{7 \times 10^9} $

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✔ Problem 2:

$ 3.6 \times 10^7 + 2.1 \times 10^7 $

- Same exponent: $10^7$
- Add coefficients: $3.6 + 2.1 = 5.7$
- Result: $5.7 \times 10^7$

✔ Answer: $ \boxed{5.7 \times 10^7} $

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✔ Problem 3:

$ 7.73 \times 10^5 - 5.3 \times 10^4 $

- Different exponents: $10^5$ vs $10^4$
- Convert $5.3 \times 10^4$ to match $10^5$:
$5.3 \times 10^4 = 0.53 \times 10^5$
- Now subtract: $7.73 \times 10^5 - 0.53 \times 10^5 = (7.73 - 0.53) \times 10^5 = 7.2 \times 10^5$

✔ Answer: $ \boxed{7.2 \times 10^5} $

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✔ Problem 4:

$ 4.9 \times 10^{10} + 5.5 \times 10^9 $

- Different exponents: $10^{10}$ vs $10^9$
- Convert $5.5 \times 10^9$ to $10^{10}$:
$5.5 \times 10^9 = 0.55 \times 10^{10}$
- Add: $4.9 \times 10^{10} + 0.55 \times 10^{10} = (4.9 + 0.55) \times 10^{10} = 5.45 \times 10^{10}$

✔ Answer: $ \boxed{5.45 \times 10^{10}} $

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✔ Problem 5:

$ 5 \times 10^{12} + 8 \times 10^{12} $

- Same exponent: $10^{12}$
- Add coefficients: $5 + 8 = 13$
- Result: $13 \times 10^{12}$
- But this is not in proper scientific notation (since 13 > 10), so convert:
$13 \times 10^{12} = 1.3 \times 10^{13}$

✔ Answer: $ \boxed{1.3 \times 10^{13}} $

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✔ Problem 6:

$ 9.8 \times 10^{14} + 3.7 \times 10^{13} $

- Different exponents: $10^{14}$ vs $10^{13}$
- Convert $3.7 \times 10^{13}$ to $10^{14}$:
$3.7 \times 10^{13} = 0.37 \times 10^{14}$
- Add: $9.8 \times 10^{14} + 0.37 \times 10^{14} = (9.8 + 0.37) \times 10^{14} = 10.17 \times 10^{14}$
- Not in proper form → convert:
$10.17 \times 10^{14} = 1.017 \times 10^{15}$

✔ Answer: $ \boxed{1.017 \times 10^{15}} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $7 \times 10^9$ |
| 2 | $5.7 \times 10^7$ |
| 3 | $7.2 \times 10^5$ |
| 4 | $5.45 \times 10^{10}$ |
| 5 | $1.3 \times 10^{13}$ |
| 6 | $1.017 \times 10^{15}$ |

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