Worksheet: Metric Conversions Name___________________ ... | Study ... - Free Printable

The image you've uploaded is a completed worksheet titled "Metric Conversions" with answers already filled in. It appears to be an answer key for a chemistry or science class, specifically from the textbook *"Chemistry: A Study of Matter"* (Episode 104). The problems involve converting between various metric and imperial units.

Let me walk through each problem and explain the solution process, including the reasoning behind each conversion.

---

1. Convert 0.057 m to km

Conversion factor:
1 km = 1000 m

Calculation:
$$
? \, \text{km} = \frac{0.057 \, \text{m}}{1} \times \frac{1 \, \text{km}}{1000 \, \text{m}} = 5.7 \times 10^{-5} \, \text{km}
$$

✔ Explanation: Since kilometers are larger than meters, we divide by 1000. Moving the decimal three places left gives $5.7 \times 10^{-5}$ km.

---

2. Convert 13 cm³ to mL

Conversion factor:
1 cm³ = 1 mL

Calculation:
$$
? \, \text{mL} = \frac{13 \, \text{cm}^3}{1} \times \frac{1 \, \text{mL}}{1 \, \text{cm}^3} = 1.3 \times 10^1 \, \text{mL}
$$

✔ Explanation: Volume-wise, cubic centimeters and milliliters are equivalent. So, 13 cm³ = 13 mL = $1.3 \times 10^1$ mL.

---

3. Convert 0.986 hours to seconds

Conversion factors:
1 hour = 60 minutes
1 minute = 60 seconds

Calculation:
$$
? \, \text{s} = \frac{0.986 \, \text{hours}}{1} \times \frac{60 \, \text{min}}{1 \, \text{hour}} \times \frac{60 \, \text{s}}{1 \, \text{min}} = 3.55 \times 10^4 \, \text{s}
$$

✔ Explanation: Multiply by 60 twice (for minutes and seconds).
$0.986 \times 3600 = 3549.6 \approx 3.55 \times 10^4$ s.

---

4. Convert 3.004 L to mL

Conversion factor:
1 L = 1000 mL

Calculation:
$$
? \, \text{mL} = \frac{3.004 \, \text{L}}{1} \times \frac{1000 \, \text{mL}}{1 \, \text{L}} = 3.004 \times 10^3 \, \text{mL}
$$

✔ Explanation: Multiply by 1000 because there are 1000 mL in a liter.

---

5. Convert 86 kg to g

Conversion factor:
1 kg = 1000 g

Calculation:
$$
? \, \text{g} = \frac{86 \, \text{kg}}{1} \times \frac{1000 \, \text{g}}{1 \, \text{kg}} = 8.6 \times 10^4 \, \text{g}
$$

✔ Explanation: Multiply by 1000 → 86,000 g = $8.6 \times 10^4$ g.

---

6. Convert 24 cm³ to L

Conversion factors:
1 cm³ = 1 mL
1000 mL = 1 L

Calculation:
$$
? \, \text{L} = \frac{24 \, \text{cm}^3}{1} \times \frac{1 \, \text{mL}}{1 \, \text{cm}^3} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 2.4 \times 10^{-2} \, \text{L}
$$

✔ Explanation: First convert cm³ → mL (same value), then divide by 1000 to get liters. 24 mL = 0.024 L = $2.4 \times 10^{-2}$ L.

---

7. Convert 56,000 μg to kg

Conversion factors:
1 μg = $10^{-6}$ g
1 kg = 1000 g

Calculation:
$$
? \, \text{kg} = \frac{56,000 \, \mu\text{g}}{1} \times \frac{1 \, \text{g}}{1,000,000 \, \mu\text{g}} \times \frac{1 \, \text{kg}}{1000 \, \text{g}} = 5.6 \times 10^{-5} \, \text{kg}
$$

✔ Explanation:
- 56,000 μg = 56,000 × $10^{-6}$ g = 0.056 g
- 0.056 g = 0.056 / 1000 = $5.6 \times 10^{-5}$ kg

---

8. Convert 56 km to mm

Conversion factors:
1 km = 1000 m
1 m = 1000 mm

Calculation:
$$
? \, \text{mm} = \frac{56 \, \text{km}}{1} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1000 \, \text{mm}}{1 \, \text{m}} = 5.6 \times 10^7 \, \text{mm}
$$

✔ Explanation: Multiply by 1000 twice → $56 \times 10^6 = 5.6 \times 10^7$ mm.

---

9. Convert 20 km to feet

This involves metric-to-imperial conversion.

Conversion factors:
1 km = 1000 m
1 m = 100 cm
1 inch = 2.54 cm
1 foot = 12 inches

Calculation:
$$
? \, \text{feet} = \frac{20 \, \text{km}}{1} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{100 \, \text{cm}}{1 \, \text{m}} \times \frac{1 \, \text{in}}{2.54 \, \text{cm}} \times \frac{1 \, \text{foot}}{12 \, \text{in}} = 7 \times 10^4 \, \text{feet}
$$

✔ Step-by-step explanation:

- 20 km = 20,000 m
- 20,000 m = 2,000,000 cm
- Convert cm to inches: $2,000,000 \div 2.54 \approx 787,401.57$ inches
- Convert inches to feet: $787,401.57 \div 12 \approx 65,616.8$ feet ≈ $6.56 \times 10^4$

But the answer given is $7 \times 10^4$, which is approximately correct (likely rounded).

> 🔍 Note: The exact value is about 65,617 ft, so rounding to $7 \times 10^4$ is acceptable for significant figures if starting value has 1 sig fig, but here 20 km has 2 sig figs. So better to write $6.6 \times 10^4$. However, the key says $7 \times 10^4$, possibly due to rounding during intermediate steps.

---

✔ Summary of Key Concepts:

- Use dimensional analysis (unit cancellation).
- Know common conversion factors:
- Length: 1 km = 1000 m, 1 m = 100 cm, 1 in = 2.54 cm, 1 ft = 12 in
- Mass: 1 kg = 1000 g, 1 g = 1000 mg, 1 μg = $10^{-6}$ g
- Volume: 1 L = 1000 mL = 1000 cm³
- Always check units cancel correctly.
- Express final answers in scientific notation when appropriate.

---

Final Answer Recap:

| Problem | Answer |
|--------|--------|
| 1 | $5.7 \times 10^{-5}$ km |
| 2 | $1.3 \times 10^1$ mL |
| 3 | $3.55 \times 10^4$ s |
| 4 | $3.004 \times 10^3$ mL |
| 5 | $8.6 \times 10^4$ g |
| 6 | $2.4 \times 10^{-2}$ L |
| 7 | $5.6 \times 10^{-5}$ kg |
| 8 | $5.6 \times 10^7$ mm |
| 9 | $7 \times 10^4$ ft |

---

Let me know if you'd like this converted into a printable PDF, or need help solving similar problems!