Completed Metric Conversion Worksheet with answers filled in for various unit conversions.

Let's go through the Metric Conversion Worksheet and verify each answer, explaining the reasoning behind the correct conversions. The metric system uses prefixes that represent powers of ten, and the standard mnemonic for remembering the order is:

K H D B D C M
(Kilo, Hecto, Deka, Base unit, Deci, Centi, Milli)

This applies to length (meters), mass (grams), and volume (liters). Moving from one unit to another involves moving the decimal point left or right depending on how many steps you're going up or down in the scale.

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✔ Let's evaluate each problem:

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1. 5 meters = ___ km

- From meters (m) to kilometers (km): move 3 places to the left (m → km)
- 5 m = 0.005 km ✔
✔ Correct

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2. 3 grams = ___ milligrams

- Grams → milligrams: move 3 places to the right (g → mg)
- 3 g = 3,000 mg ✘
✘ Incorrect – Answer should be 3,000, not 0.003

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3. 7 meters = ___ cm

- Meters → centimeters: move 2 places to the right (m → cm)
- 7 m = 700 cm ✘
✘ Incorrect – Answer should be 700, not 0.07

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4. 60 milligrams = ___ km

- This is invalid — milligrams (mass) cannot be converted to kilometers (length).
✘ Wrong conversion type – Cannot convert mg to km

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5. 2.5 meters = ___ mm

- Meters → millimeters: move 3 places to the right
- 2.5 m = 2,500 mm ✘
✘ Incorrect – Answer should be 2,500, not 0.0025

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6. 4.5 centimeters = ___ km

- Centimeters → kilometers: move 5 places to the left
- 4.5 cm = 0.000045 km ✘
✘ Incorrect – Answer should be 0.000045, not 45,000

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7. 77 meters = ___ dm

- Meters → decimeters: move 1 place to the right (m → dm)
- 77 m = 770 dm ✘
✘ Incorrect – Answer should be 770, not 7.7

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8. 37 decimeters = ___ mm

- Decimeters → millimeters: move 2 places to the right (dm → mm)
- 37 dm = 3,700 mm ✘
✘ Incorrect – Answer should be 3,700, not 0.037

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9. 0.002 centimeters = ___ mm

- Centimeters → millimeters: move 1 place to the right (cm → mm)
- 0.002 cm = 0.02 mm ✘
✘ Incorrect – Answer should be 0.02, not 0.0002

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10. 44 millimeters = ___ m

- Millimeters → meters: move 3 places to the left
- 44 mm = 0.044 m ✔
✔ Correct

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11. 25 kilometers = ___ m

- Kilometers → meters: move 3 places to the right
- 25 km = 25,000 m ✘
✘ Incorrect – Answer should be 25,000, not 0.025

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12. 880 meters = ___ cm

- Meters → centimeters: move 2 places to the right
- 880 m = 88,000 cm ✘
✘ Incorrect – Answer should be 88,000, not 8.80

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13. 9.5 kiloliters = ___ deciliters

- Kiloliters → deciliters:
- kL → L: ×1000
- L → dL: ×10
- So kL → dL: ×10,000
- 9.5 kL = 9.5 × 10,000 = 95,000 dL ✘
✘ Incorrect – Answer should be 95,000, not 0.95

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14. 66 decimeters = ___ decameters

- Decimeters → decameters:
- dm → m: ÷10
- m → dam: ÷10
- So dm → dam: ÷100
- 66 dm = 0.66 dam ✔
✔ Correct

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15. 5 liters = ___ hectoliters

- Liters → hectoliters: move 2 places to the left (L → hL)
- 5 L = 0.05 hL ✔
✔ Correct

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✔ Summary of Correct Answers:

| Problem | Correct Answer |
|--------|----------------|
| 1 | 0.005 km ✔ |
| 2 | 3,000 mg ✘ (given: 0.003) |
| 3 | 700 cm ✘ (given: 0.07) |
| 4 | Invalid (mg → km) ✘ |
| 5 | 2,500 mm ✘ (given: 0.0025) |
| 6 | 0.000045 km ✘ (given: 45,000) |
| 7 | 770 dm ✘ (given: 7.7) |
| 8 | 3,700 mm ✘ (given: 0.037) |
| 9 | 0.02 mm ✘ (given: 0.0002) |
| 10 | 0.044 m ✔ |
| 11 | 25,000 m ✘ (given: 0.025) |
| 12 | 88,000 cm ✘ (given: 8.80) |
| 13 | 95,000 dL ✘ (given: 0.95) |
| 14 | 0.66 dam ✔ |
| 15 | 0.05 hL ✔ |

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🔍 Key Mistakes Identified:

- Wrong direction: Many answers moved the decimal the wrong way.
- Wrong magnitude: Some used incorrect number of decimal places.
- Invalid units: Converting between incompatible units (e.g., mg → km).
- Misunderstanding prefix values: For example, kilo = 1000, not 0.001.

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📌 Tips for Success:

1. Use the KHD B DCM chart:
- K (kilo) → H (hecto) → D (deka) → B (base) → D (deci) → C (centi) → M (milli)
2. Count how many steps between units.
3. Move decimal point right when going to smaller units (down), left when going to larger units (up).
4. Never convert across different measurement types (mass ↔ length).

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✔ Final Answer: Only problems 1, 10, 14, and 15 are correct as written.

The rest contain significant errors in conversion logic or magnitude.

Let me know if you'd like a corrected version of the worksheet!