Let's solve each of these metric conversion problems step by step. We'll use the standard metric prefixes and their relationships:
Metric Prefixes (from largest to smallest):
-
kilo (k) = 10³
-
hecto (h) = 10²
-
deca (da) = 10¹
-
base unit (g, m, L)
-
deci (d) = 10⁻¹
-
centi (c) = 10⁻²
-
milli (m) = 10⁻³
-
micro (μ) = 10⁻⁶ (not used here)
Also:
- 1 cm³ = 1 mL
- 1 cc = 1 mL = 1 cm³
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Now, let’s go through each problem:
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1. 36.52 mg = ________ g
- milligram → gram: divide by 1000 (since 1 g = 1000 mg)
- $ 36.52 \div 1000 = 0.03652 $
-
✔ 0.03652 g
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2. 14.72 kg = ________ mg
- kilogram → milligram: multiply by 1,000,000 (1 kg = 1000 g, 1 g = 1000 mg → 1 kg = 10⁶ mg)
- $ 14.72 \times 1,000,000 = 14,720,000 $
-
✔ 14,720,000 mg
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3. 0.0035 hm = ________ dm
- hectometer (hm) → decimeter (dm)
- 1 hm = 100 m, 1 m = 10 dm → so 1 hm = 100 × 10 = 1000 dm
- So, $ 0.0035 \times 1000 = 3.5 $
-
✔ 3.5 dm
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4. 0.134 m = ________ km
- meter → kilometer: divide by 1000
- $ 0.134 \div 1000 = 0.000134 $
-
✔ 0.000134 km
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5. 25 mm = ________ cm
- millimeter → centimeter: divide by 10 (1 cm = 10 mm)
- $ 25 \div 10 = 2.5 $
-
✔ 2.5 cm
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6. 2.5 cm³ = ________ mL
- 1 cm³ = 1 mL
-
✔ 2.5 mL
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7. 243 daL = ________ L
- dekaliter → liter: 1 daL = 10 L
- $ 243 \times 10 = 2430 $
-
✔ 2430 L
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8. 45.23 L = ________ mL
- liter → milliliter: multiply by 1000
- $ 45.23 \times 1000 = 45,230 $
-
✔ 45,230 mL
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9. 0.035 hL = ________ cL
- hectoliter → centiliter
- 1 hL = 100 L, 1 L = 100 cL → 1 hL = 100 × 100 = 10,000 cL
- $ 0.035 \times 10,000 = 350 $
-
✔ 350 cL
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10. 27.32 mm = ________ m
- millimeter → meter: divide by 1000
- $ 27.32 \div 1000 = 0.02732 $
-
✔ 0.02732 m
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11. 15 m = ________ dm
- meter → decimeter: multiply by 10 (1 m = 10 dm)
- $ 15 \times 10 = 150 $
-
✔ 150 dm
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12. 0.023 cc = ________ L
- cc = cubic centimeter = mL
- 1 mL = 0.001 L
- $ 0.023 \times 0.001 = 0.000023 $
-
✔ 0.000023 L
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13. 0.00049 km = ________ mm
- kilometer → millimeter: 1 km = 1,000 m, 1 m = 1000 mm → 1 km = 1,000,000 mm
- $ 0.00049 \times 1,000,000 = 490 $
-
✔ 490 mm
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14. 0.025 kg = ________ g
- kilogram → gram: multiply by 1000
- $ 0.025 \times 1000 = 25 $
-
✔ 25 g
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15. 15 g = ________ hg
- gram → hectogram: divide by 100 (1 hg = 100 g)
- $ 15 \div 100 = 0.15 $
-
✔ 0.15 hg
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Final Answers:
1.
0.03652 g
2.
14,720,000 mg
3.
3.5 dm
4.
0.000134 km
5.
2.5 cm
6.
2.5 mL
7.
2430 L
8.
45,230 mL
9.
350 cL
10.
0.02732 m
11.
150 dm
12.
0.000023 L
13.
490 mm
14.
25 g
15.
0.15 hg
✔ All conversions completed!
Let me know if you'd like this in a printable format or with explanations for any specific one!
Parent Tip: Review the logic above to help your child master the concept of metric system conversion worksheet chemistry.
