Scientific notation practice worksheet with problems and answer key for coloring.

Let’s solve each problem step by step. We’ll multiply or divide the numbers and handle the powers of 10 separately, then combine them.

---

Problem 1:
(3.2 × 10⁵)(5.6 × 10³)
→ Multiply coefficients: 3.2 × 5.6 = 17.92
→ Add exponents: 10⁵ × 10³ = 10⁸
→ So we have 17.92 × 10⁸ → but this is not in proper scientific notation (coefficient should be between 1 and 10).
→ Convert: 17.92 × 10⁸ = 1.792 × 10⁹

✔ Final Answer for #1: 1.792 × 10⁹

---

Problem 2:
(7/4) × (10⁶ / 10⁴)
→ First, 7 ÷ 4 = 1.75
→ Then, 10⁶ ÷ 10⁴ = 10²
→ So: 1.75 × 10²

✔ Final Answer for #2: 1.75 × 10²

---

Problem 3:
(9 × 10⁵)(2.56 × 10²)
→ Multiply coefficients: 9 × 2.56 = 23.04
→ Add exponents: 10⁵ × 10² = 10⁷
→ 23.04 × 10⁷ → convert to proper form: 2.304 × 10⁸

✔ Final Answer for #3: 2.304 × 10⁸

---

Problem 4:
(2.4 × 10¹²) / (16 × 10⁵)
→ Divide coefficients: 2.4 ÷ 16 = 0.15
→ Subtract exponents: 10¹² ÷ 10⁵ = 10⁷
→ So: 0.15 × 10⁷ → convert: 1.5 × 10⁶

✔ Final Answer for #4: 1.5 × 10⁶

---

Problem 5:
(5.16 × 10⁻⁴)(8 × 10³)
→ Multiply coefficients: 5.16 × 8 = 41.28
→ Add exponents: 10⁻⁴ × 10³ = 10⁻¹
→ 41.28 × 10⁻¹ → convert: 4.128 × 10⁰ (which is just 4.128)
But let’s keep it as scientific notation: 4.128 × 10⁰ — though usually we write whole numbers without exponent if it’s 10⁰. But since the format expects scientific notation, we can leave it as 4.128 × 10⁰. However, sometimes they prefer coefficient ≥1 and <10, so 4.128 × 10⁰ is fine. Alternatively, you could say 4.128, but let’s stick with scientific notation.

Wait — actually, 41.28 × 10⁻¹ = 4.128 × 10⁰ — yes.

✔ Final Answer for #5: 4.128 × 10⁰

*(Note: Some might write this as 4.128, but since the worksheet uses scientific notation, we'll keep the exponent.)*

---

Problem 6:
(18.9 × 10⁷) / (1.25 × 10²)
→ Divide coefficients: 18.9 ÷ 1.25 = 15.12
→ Subtract exponents: 10⁷ ÷ 10² = 10⁵
→ 15.12 × 10⁵ → convert: 1.512 × 10⁶

✔ Final Answer for #6: 1.512 × 10⁶

---

Problem 7:
(86 × 10⁻²)(7 × 10⁵)
→ Multiply coefficients: 86 × 7 = 602
→ Add exponents: 10⁻² × 10⁵ = 10³
→ 602 × 10³ → convert: 6.02 × 10⁵

✔ Final Answer for #7: 6.02 × 10⁵

---

Problem 8:
(5.22 × 10⁶) / (2 × 10⁻³)
→ Divide coefficients: 5.22 ÷ 2 = 2.61
→ Subtract exponents: 10⁶ ÷ 10⁻³ = 10⁹ (because 6 - (-3) = 9)
→ So: 2.61 × 10⁹

✔ Final Answer for #8: 2.61 × 10⁹

---

Problem 9:
(7.22 × 10⁶)(8 × 10⁻⁴)
→ Multiply coefficients: 7.22 × 8 = 57.76
→ Add exponents: 10⁶ × 10⁻⁴ = 10²
→ 57.76 × 10² → convert: 5.776 × 10³

✔ Final Answer for #9: 5.776 × 10³

---

Problem 10:
(5.9 × 10⁵) / (625 × 10⁻²)
→ First, rewrite denominator: 625 × 10⁻² = 6.25 × 10² (since 625 = 6.25 × 10², so 6.25 × 10² × 10⁻² = 6.25 × 10⁰? Wait — no.)

Actually, better to do:

Numerator: 5.9 × 10⁵
Denominator: 625 × 10⁻² = 6.25 × 10² × 10⁻²? No — 625 = 6.25 × 10², so 625 × 10⁻² = 6.25 × 10² × 10⁻² = 6.25 × 10⁰ = 6.25

So now: (5.9 × 10⁵) / 6.25
→ 5.9 ÷ 6.25 = 0.944
→ So: 0.944 × 10⁵ → convert: 9.44 × 10⁴

Alternatively, do it all at once:

(5.9 × 10⁵) / (625 × 10⁻²) = (5.9 / 625) × 10^(5 - (-2)) = (5.9 / 625) × 10⁷
5.9 ÷ 625 = 0.00944
Then 0.00944 × 10⁷ = 9.44 × 10⁴

Yes.

✔ Final Answer for #10: 9.44 × 10⁴

---

Problem 11:
(9 × 10⁻³)(13 × 10⁵)
→ Multiply coefficients: 9 × 13 = 117
→ Add exponents: 10⁻³ × 10⁵ = 10²
→ 117 × 10² → convert: 1.17 × 10⁴

✔ Final Answer for #11: 1.17 × 10⁴

---

Problem 12:
(5 × 10⁻⁵) / (2 × 10⁶)
→ Divide coefficients: 5 ÷ 2 = 2.5
→ Subtract exponents: 10⁻⁵ ÷ 10⁶ = 10⁻¹¹
→ So: 2.5 × 10⁻¹¹

✔ Final Answer for #12: 2.5 × 10⁻¹¹

---

Problem 13:
(24 × 10⁶)(6.1 × 10)
→ Note: 10 = 10¹
→ Multiply coefficients: 24 × 6.1 = 146.4
→ Add exponents: 10⁶ × 10¹ = 10⁷
→ 146.4 × 10⁷ → convert: 1.464 × 10⁹

✔ Final Answer for #13: 1.464 × 10⁹

---

Problem 14:
(7.2 × 10¹¹) / (8 × 10⁶)
→ Divide coefficients: 7.2 ÷ 8 = 0.9
→ Subtract exponents: 10¹¹ ÷ 10⁶ = 10⁵
→ 0.9 × 10⁵ → convert: 9 × 10⁴

✔ Final Answer for #14: 9 × 10⁴

---

Problem 15:
(1.7 × 10)(1.4 × 10²)
→ First, 1.7 × 1.4 = 2.38
→ Exponents: 10¹ × 10² = 10³
→ So: 2.38 × 10³

✔ Final Answer for #15: 2.38 × 10³

---

Final Answers Summary:

1. 1.792 × 10⁹
2. 1.75 × 10²
3. 2.304 × 10⁸
4. 1.5 × 10⁶
5. 4.128 × 10⁰
6. 1.512 × 10⁶
7. 6.02 × 10⁵
8. 2.61 × 10⁹
9. 5.776 × 10³
10. 9.44 × 10⁴
11. 1.17 × 10⁴
12. 2.5 × 10⁻¹¹
13. 1.464 × 10⁹
14. 9 × 10⁴
15. 2.38 × 10³

──────────────────────────────────────

Final Answer:
1. 1.792 × 10⁹
2. 1.75 × 10²
3. 2.304 × 10⁸
4. 1.5 × 10⁶
5. 4.128 × 10⁰
6. 1.512 × 10⁶
7. 6.02 × 10⁵
8. 2.61 × 10⁹
9. 5.776 × 10³
10. 9.44 × 10⁴
11. 1.17 × 10⁴
12. 2.5 × 10⁻¹¹
13. 1.464 × 10⁹
14. 9 × 10⁴
15. 2.38 × 10³