Operations With Numbers in Scientific Notation | Worksheet ... - Free Printable

Absolutely! Let’s solve the problems step by step. The worksheet has two sections:

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## ✔ SECTION 1: ADD OR SUBTRACT — Write each answer in scientific notation.

Important note: To add or subtract numbers in scientific notation, they must have the same exponent. If not, convert one (or both) so they match, then add/subtract the coefficients and keep the exponent.

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1. `(3.58 × 10⁴) + (2.12 × 10⁵)`

→ Convert `3.58 × 10⁴` to `0.358 × 10⁵`
→ Now: `0.358 × 10⁵ + 2.12 × 10⁵ = (0.358 + 2.12) × 10⁵ = 2.478 × 10⁵`

✔ Answer: `2.478 × 10⁵`

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2. `(6.56 × 10⁷) - (4.25 × 10⁶)`

→ Convert `4.25 × 10⁶` to `0.425 × 10⁷`
→ Now: `6.56 × 10⁷ - 0.425 × 10⁷ = (6.56 - 0.425) × 10⁷ = 6.135 × 10⁷`

✔ Answer: `6.135 × 10⁷`

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3. `(9.56 × 10³) - (5.8 × 10²)`

→ Convert `5.8 × 10²` to `0.58 × 10³`
→ Now: `9.56 × 10³ - 0.58 × 10³ = (9.56 - 0.58) × 10³ = 8.98 × 10³`

✔ Answer: `8.98 × 10³`

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4. `(4.83 × 10⁴) + (1.9 × 10³)`

→ Convert `1.9 × 10³` to `0.19 × 10⁴`
→ Now: `4.83 × 10⁴ + 0.19 × 10⁴ = (4.83 + 0.19) × 10⁴ = 5.02 × 10⁴`

✔ Answer: `5.02 × 10⁴`

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5. `(1.75 × 10⁻³) - (6.12 × 10⁻⁴)`

→ Convert `6.12 × 10⁻⁴` to `0.612 × 10⁻³`
→ Now: `1.75 × 10⁻³ - 0.612 × 10⁻³ = (1.75 - 0.612) × 10⁻³ = 1.138 × 10⁻³`

✔ Answer: `1.138 × 10⁻³`

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6. `(5.63 × 10⁻⁵) + (4.02 × 10⁻⁶)`

→ Convert `4.02 × 10⁻⁶` to `0.402 × 10⁻⁵`
→ Now: `5.63 × 10⁻⁵ + 0.402 × 10⁻⁵ = (5.63 + 0.402) × 10⁻⁵ = 6.032 × 10⁻⁵`

✔ Answer: `6.032 × 10⁻⁵`

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7. `(7.82 × 10⁸) + (8.4 × 10⁷)`

→ Convert `8.4 × 10⁷` to `0.84 × 10⁸`
→ Now: `7.82 × 10⁸ + 0.84 × 10⁸ = (7.82 + 0.84) × 10⁸ = 8.66 × 10⁸`

✔ Answer: `8.66 × 10⁸`

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8. `(3.2 × 10⁻⁴) - (5.8 × 10⁻⁵)`

→ Convert `5.8 × 10⁻⁵` to `0.58 × 10⁻⁴`
→ Now: `3.2 × 10⁻⁴ - 0.58 × 10⁻⁴ = (3.2 - 0.58) × 10⁻⁴ = 2.62 × 10⁻⁴`

✔ Answer: `2.62 × 10⁻⁴`

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## ✔ SECTION 2: MULTIPLY OR DIVIDE — Write each answer in scientific notation.

Rules:
- Multiply: multiply coefficients, add exponents.
- Divide: divide coefficients, subtract exponents.
- Then adjust to proper scientific notation (coefficient between 1 and 10).

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1. `(8.5 × 10⁷) / (2.5 × 10⁴)`

→ Coefficients: `8.5 ÷ 2.5 = 3.4`
→ Exponents: `10⁷ ÷ 10⁴ = 10³`
→ Result: `3.4 × 10³`

✔ Answer: `3.4 × 10³`

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2. `(1.3 × 10⁵) × (7.2 × 10³)`

→ Coefficients: `1.3 × 7.2 = 9.36`
→ Exponents: `10⁵ × 10³ = 10⁸`
→ Result: `9.36 × 10⁸`

✔ Answer: `9.36 × 10⁸`

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3. `(2.14 × 10⁵) × (3.5 × 10²)`

→ Coefficients: `2.14 × 3.5 = 7.49`
→ Exponents: `10⁵ × 10² = 10⁷`
→ Result: `7.49 × 10⁷`

✔ Answer: `7.49 × 10⁷`

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4. `(9.12 × 10⁻⁷) / (4 × 10⁻⁹)`

→ Coefficients: `9.12 ÷ 4 = 2.28`
→ Exponents: `10⁻⁷ ÷ 10⁻⁹ = 10²`
→ Result: `2.28 × 10²`

✔ Answer: `2.28 × 10²`

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5. `(4.5 × 10⁶) × (6.6 × 10⁻³)`

→ Coefficients: `4.5 × 6.6 = 29.7`
→ Exponents: `10⁶ × 10⁻³ = 10³`
→ Result: `29.7 × 10³` → Adjust to scientific notation: `2.97 × 10⁴`

✔ Answer: `2.97 × 10⁴`

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6. `(5.7 × 10⁴) ÷ (4.3 × 10³)`

→ Coefficients: `5.7 ÷ 4.3 ≈ 1.32558...` → Round to 3 significant figures? Since inputs have 2 sig figs, we can use 2: `1.3`
→ Exponents: `10⁴ ÷ 10³ = 10¹`
→ Result: `1.3 × 10¹`

✔ Answer: `1.3 × 10¹`

*(Note: If more precision is allowed, you could write `1.33 × 10¹`, but since 5.7 and 4.3 both have 2 sig figs, 1.3 is appropriate.)*

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7. `(3.8 × 10⁻⁶) / (2.5 × 10⁻⁸)`

→ Coefficients: `3.8 ÷ 2.5 = 1.52`
→ Exponents: `10⁻⁶ ÷ 10⁻⁸ = 10²`
→ Result: `1.52 × 10²`

✔ Answer: `1.52 × 10²`

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8. `(3.02 × 10⁵) / (4.2 × 10⁴)`

→ Coefficients: `3.02 ÷ 4.2 ≈ 0.719...`
→ Exponents: `10⁵ ÷ 10⁴ = 10¹`
→ Result: `0.719 × 10¹` → Adjust to scientific notation: `7.19 × 10⁰`

✔ Answer: `7.19 × 10⁰`

*(Note: 7.19 × 10⁰ is just 7.19, but it's still correct in scientific notation.)*

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## 📝 Final Answers Summary:

Add/Subtract:

1. `2.478 × 10⁵`
2. `6.135 × 10⁷`
3. `8.98 × 10³`
4. `5.02 × 10⁴`
5. `1.138 × 10⁻³`
6. `6.032 × 10⁻⁵`
7. `8.66 × 10⁸`
8. `2.62 × 10⁻⁴`

Multiply/Divide:

1. `3.4 × 10³`
2. `9.36 × 10⁸`
3. `7.49 × 10⁷`
4. `2.28 × 10²`
5. `2.97 × 10⁴`
6. `1.3 × 10¹`
7. `1.52 × 10²`
8. `7.19 × 10⁰`

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