Sure! Let’s solve each conversion problem step by step. These are metric unit conversions, so we’ll use the standard metric prefixes and their relationships.
---
Metric Prefixes (for reference):
Length:
- km (kilometer) = 1000 m
- hm (hectometer) = 100 m
- dam (decameter) = 10 m
- m (meter)
- dm (decimeter) = 0.1 m
- cm (centimeter) = 0.01 m
- mm (millimeter) = 0.001 m
Mass:
- kg (kilogram) = 1000 g
- hg (hectogram) = 100 g
- dag (decagram) = 10 g
- g (gram)
- dg (decigram) = 0.1 g
- cg (centigram) = 0.01 g
- mg (milligram) = 0.001 g
Volume:
- kl (kiloliter) = 1000 L
- hl (hectoliter) = 100 L
- dal (decaliter) = 10 L
- L (liter)
- dl (deciliter) = 0.1 L
- cl (centiliter) = 0.01 L
- ml (milliliter) = 0.001 L
---
##
✔ SOLUTIONS:
---
1 a. 32 dg = ______ g
→ 1 dg = 0.1 g → 32 × 0.1 =
3.2 g
1 b. 8 g = ______ cg
→ 1 g = 100 cg → 8 × 100 =
800 cg
---
2 a. 59 g = ______ dag
→ 1 dag = 10 g → 59 ÷ 10 =
5.9 dag
2 b. 1 hg = ______ dg
→ 1 hg = 100 g, 1 g = 10 dg → 100 × 10 =
1,000 dg
---
3 a. 12 hm = ______ km
→ 1 km = 10 hm → 12 ÷ 10 =
1.2 km
3 b. 9 km = ______ dam
→ 1 km = 100 dam → 9 × 100 =
900 dam
---
4 a. 7.3 kg = ______ dag
→ 1 kg = 1000 g, 1 dag = 10 g → 1 kg = 100 dag → 7.3 × 100 =
730 dag
4 b. 1,600 mg = ______ g
→ 1 g = 1000 mg → 1600 ÷ 1000 =
1.6 g
---
5 a. 5 dm = ______ mm
→ 1 dm = 100 mm → 5 × 100 =
500 mm
5 b. 480 m = ______ hm
→ 1 hm = 100 m → 480 ÷ 100 =
4.8 hm
---
6 a. 9.8 cm = ______ mm
→ 1 cm = 10 mm → 9.8 × 10 =
98 mm
6 b. 7 hl = ______ dl
→ 1 hl = 100 L, 1 L = 10 dl → 1 hl = 1000 dl → 7 × 1000 =
7,000 dl
---
7 a. 10 cg = ______ dg
→ 1 dg = 10 cg → 10 ÷ 10 =
1 dg
7 b. 9 dam = ______ m
→ 1 dam = 10 m → 9 × 10 =
90 m
---
8 a. 6 hl = ______ L
→ 1 hl = 100 L → 6 × 100 =
600 L
8 b. 5.4 m = ______ cm
→ 1 m = 100 cm → 5.4 × 100 =
540 cm
---
9 a. 7.6 kl = ______ hl
→ 1 kl = 10 hl → 7.6 × 10 =
76 hl
9 b. 4.9 dag = ______ dg
→ 1 dag = 100 dg → 4.9 × 100 =
490 dg
---
10 a. 10 hl = ______ dl
→ 1 hl = 1000 dl → 10 × 1000 =
10,000 dl
10 b. 1,000 cm = ______ dam
→ 1 dam = 1000 cm → 1000 ÷ 1000 =
1 dam
---
## 📝 Final Answers:
1a. 3.2 g
1b. 800 cg
2a. 5.9 dag
2b. 1,000 dg
3a. 1.2 km
3b. 900 dam
4a. 730 dag
4b. 1.6 g
5a. 500 mm
5b. 4.8 hm
6a. 98 mm
6b. 7,000 dl
7a. 1 dg
7b. 90 m
8a. 600 L
8b. 540 cm
9a. 76 hl
9b. 490 dg
10a. 10,000 dl
10b. 1 dam
---
✔ All problems solved using metric conversion rules. You can always remember: moving left in the metric scale divides by 10 for each step; moving right multiplies by 10 for each step.
Let me know if you’d like a visual chart or mnemonic to help remember these conversions!
Parent Tip: Review the logic above to help your child master the concept of converting metric units worksheet 5th grade.