Let's solve each of the metric conversion problems step by step, using the
metric ladder and the rules provided:
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🔁 Conversion Rules Recap:
-
To convert to a smaller unit: Move decimal point
right (multiply)
-
To convert to a larger unit: Move decimal point
left (divide)
The metric prefixes in order from largest to smallest:
>
Kilo → Hecto → Deka → Basic Unit → Deci → Centi → Milli
Memory trick:
"King Henry Died Monday Drinking Chocolate Milk"
→ Kilo, Hecto, Deka,
(Base), Deci, Centi, Milli
Each step is a factor of
10, so moving one step = multiply/divide by 10.
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Now let’s solve each problem:
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1) 3000 mg = ________ g
-
mg → g: Move from milli to base (grams), which is
3 steps up (milli → centi → deci → base).
- So divide by 1000.
- $ 3000 \div 1000 = 3 $
-
✔ 3 g
---
2) 105 km = ________ m
-
km → m: Move from kilo to base (meters),
3 steps down (kilo → hecto → deka → meter).
- Multiply by 1000.
- $ 105 \times 1000 = 105,000 $
-
✔ 105,000 m
---
3) 500 cm = ________ m
-
cm → m: Move from centi to base (meters),
2 steps up (centi → deci → meter).
- Divide by 100.
- $ 500 \div 100 = 5 $
-
✔ 5 m
---
4) 15.6 kg = ________ g
-
kg → g: Move from kilo to base (grams),
3 steps down.
- Multiply by 1000.
- $ 15.6 \times 1000 = 15,600 $
-
✔ 15,600 g
---
5) 10 mm = ________ cm
-
mm → cm: Move from milli to centi,
1 step up.
- Divide by 10.
- $ 10 \div 10 = 1 $
-
✔ 1 cm
---
6) 7 L = ________ mL
-
L → mL: Liter is the base unit; mL is milli-liter → 3 steps down.
- Multiply by 1000.
- $ 7 \times 1000 = 7000 $
-
✔ 7000 mL
---
7) 198 g = ________ kg
-
g → kg: Move from base to kilo,
3 steps up.
- Divide by 1000.
- $ 198 \div 1000 = 0.198 $
-
✔ 0.198 kg
---
8) 65 mL = ________ L
-
mL → L: Move from milli to base,
3 steps up.
- Divide by 1000.
- $ 65 \div 1000 = 0.065 $
-
✔ 0.065 L
---
9) 60 cm = ________ m
-
cm → m: 2 steps up (centi → deci → meter).
- Divide by 100.
- $ 60 \div 100 = 0.6 $
-
✔ 0.6 m
---
10) 7.6 m = ________ cm
-
m → cm: 2 steps down (meter → deci → centi).
- Multiply by 100.
- $ 7.6 \times 100 = 760 $
-
✔ 760 cm
---
11) 19 cm = ________ mm
-
cm → mm: 1 step down (centi → milli).
- Multiply by 10.
- $ 19 \times 10 = 190 $
-
✔ 190 mm
---
12) 1500 m = ________ km
-
m → km: 3 steps up (meter → deka → hecto → kilo).
- Divide by 1000.
- $ 1500 \div 1000 = 1.5 $
-
✔ 1.5 km
---
13) 25 g = ________ mg
-
g → mg: 3 steps down (gram → decigram → centigram → milligram).
- Multiply by 1000.
- $ 25 \times 1000 = 25,000 $
-
✔ 25,000 mg
---
14) 8.3 cm = ________ mm
-
cm → mm: 1 step down.
- Multiply by 10.
- $ 8.3 \times 10 = 83 $
-
✔ 83 mm
---
15) 130 mg = ________ g
-
mg → g: 3 steps up.
- Divide by 1000.
- $ 130 \div 1000 = 0.13 $
-
✔ 0.13 g
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1) 3000 mg = |
3 g |
| 2) 105 km = |
105,000 m |
| 3) 500 cm = |
5 m |
| 4) 15.6 kg = |
15,600 g |
| 5) 10 mm = |
1 cm |
| 6) 7 L = |
7000 mL |
| 7) 198 g = |
0.198 kg |
| 8) 65 mL = |
0.065 L |
| 9) 60 cm = |
0.6 m |
| 10) 7.6 m = |
760 cm |
| 11) 19 cm = |
190 mm |
| 12) 1500 m = |
1.5 km |
| 13) 25 g = |
25,000 mg |
| 14) 8.3 cm = |
83 mm |
| 15) 130 mg = |
0.13 g |
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📌 Tips for Success:
- Use the
ladder method: Count how many steps you move and adjust decimal accordingly.
- Remember:
Multiply when going down,
Divide when going up.
- Use the mnemonic:
KHD M DCMM (King Henry Died Monday Drinking Chocolate Milk).
Let me know if you'd like this as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of metric system conversions worksheets.
