Math worksheet for practicing addition and subtraction of numbers in scientific notation.

Let's solve the problems on this worksheet step by step. The goal is to add or subtract numbers in scientific notation, and then express the result in proper scientific notation.

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🔧 Key Rules for Adding/Subtracting Scientific Notation:

1. Make sure both numbers have the same power of 10.
2. If they don’t, rewrite one (or both) so that they do.
3. Apply the distributive property: $ a \times 10^n + b \times 10^n = (a + b) \times 10^n $
4. Simplify and write the final answer in scientific notation (coefficient between 1 and 10).

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✔ Example Problem (from the instructions):

> $(5.04 \times 10^3) + (3.7 \times 10^2)$

#### Step 1: Make powers of 10 the same
We need both numbers to have the same exponent. Let's convert $3.7 \times 10^2$ to $10^3$:

$$
3.7 \times 10^2 = 0.37 \times 10^3
$$

Now:
$$
(5.04 \times 10^3) + (0.37 \times 10^3) = (5.04 + 0.37) \times 10^3 = 5.41 \times 10^3
$$

✔ Final Answer: $ \boxed{5.41 \times 10^3} $

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Now let’s go through each problem on the worksheet.

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📝 Problems to Solve:

#### 1. $ (2.6 \times 10^3) + (4.2 \times 10^3) $

Same power of 10 → Add coefficients:

$$
(2.6 + 4.2) \times 10^3 = 6.8 \times 10^3
$$

✔ Answer: $ \boxed{6.8 \times 10^3} $

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#### 2. $ (3.54 \times 10^7) - (1.39 \times 10^7) $

Same power → Subtract:

$$
(3.54 - 1.39) \times 10^7 = 2.15 \times 10^7
$$

✔ Answer: $ \boxed{2.15 \times 10^7} $

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#### 3. $ (7.43 \times 10^5) + (3.89 \times 10^5) $

Same power → Add:

$$
(7.43 + 3.89) \times 10^5 = 11.32 \times 10^5
$$

But this is not in scientific notation! Coefficient must be < 10.

So convert:
$$
11.32 \times 10^5 = 1.132 \times 10^6
$$

✔ Answer: $ \boxed{1.132 \times 10^6} $

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#### 4. $ (5.94 \times 10^6) - (3.6 \times 10^6) $

Same power → Subtract:

$$
(5.94 - 3.6) \times 10^6 = 2.34 \times 10^6
$$

✔ Answer: $ \boxed{2.34 \times 10^6} $

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#### 5. $ (1.98 \times 10^5) - (6.95 \times 10^4) $

Different exponents. Convert $6.95 \times 10^4$ to $10^5$:

$$
6.95 \times 10^4 = 0.695 \times 10^5
$$

Now subtract:

$$
(1.98 - 0.695) \times 10^5 = 1.285 \times 10^5
$$

✔ Answer: $ \boxed{1.285 \times 10^5} $

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#### 6. $ (6.70 \times 10^4) + (2.05 \times 10^3) $

Convert $2.05 \times 10^3$ to $10^4$:

$$
2.05 \times 10^3 = 0.205 \times 10^4
$$

Add:

$$
(6.70 + 0.205) \times 10^4 = 6.905 \times 10^4
$$

✔ Answer: $ \boxed{6.905 \times 10^4} $

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#### 7. $ (6.83 \times 10^8) + (1.07 \times 10^7) $

Convert $1.07 \times 10^7$ to $10^8$:

$$
1.07 \times 10^7 = 0.107 \times 10^8
$$

Add:

$$
(6.83 + 0.107) \times 10^8 = 6.937 \times 10^8
$$

✔ Answer: $ \boxed{6.937 \times 10^8} $

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#### 8. $ (8.31 \times 10^6) - (7.63 \times 10^5) $

Convert $7.63 \times 10^5$ to $10^6$:

$$
7.63 \times 10^5 = 0.763 \times 10^6
$$

Subtract:

$$
(8.31 - 0.763) \times 10^6 = 7.547 \times 10^6
$$

✔ Answer: $ \boxed{7.547 \times 10^6} $

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#### 9. $ (6.8 \times 10^2) + (3.94 \times 10^1) $

Convert $3.94 \times 10^1$ to $10^2$:

$$
3.94 \times 10^1 = 0.394 \times 10^2
$$

Add:

$$
(6.8 + 0.394) \times 10^2 = 7.194 \times 10^2
$$

✔ Answer: $ \boxed{7.194 \times 10^2} $

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#### 10. $ (3.05 \times 10^6) - (9.4 \times 10^5) $

Convert $9.4 \times 10^5$ to $10^6$:

$$
9.4 \times 10^5 = 0.94 \times 10^6
$$

Subtract:

$$
(3.05 - 0.94) \times 10^6 = 2.11 \times 10^6
$$

✔ Answer: $ \boxed{2.11 \times 10^6} $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $6.8 \times 10^3$ |
| 2 | $2.15 \times 10^7$ |
| 3 | $1.132 \times 10^6$ |
| 4 | $2.34 \times 10^6$ |
| 5 | $1.285 \times 10^5$ |
| 6 | $6.905 \times 10^4$ |
| 7 | $6.937 \times 10^8$ |
| 8 | $7.547 \times 10^6$ |
| 9 | $7.194 \times 10^2$ |
| 10 | $2.11 \times 10^6$ |

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Let me know if you'd like these written out in a printable format or with more explanation!