In Grade 4 you converted larger units to smaller ones, like feet to inches. Metric units are built on powers of ten, so converting them is a matter of moving digits.
Key idea
Going from a bigger unit to a smaller one, multiply: there will be more of the small units. Going from a smaller unit to a bigger one, divide. In a problem with two units, change to one unit before you calculate.
Why it works
One meter is 100 centimeters, so 3 meters is 3 groups of 100 centimeters: $3 \times 100 = 300$. Going back, 300 centimeters holds 100 centimeters 3 times: $300 \div 100 = 3$. The amount never changes; only the size of the unit you count with changes.
| Metric | Customary |
|---|---|
| 1 km = 1,000 m | 1 ft = 12 in |
| 1 m = 100 cm | 1 yd = 3 ft |
| 1 cm = 10 mm | 1 lb = 16 oz |
| 1 kg = 1,000 g | 1 gal = 4 qt; 1 qt = 2 pt; 1 pt = 2 c |
| 1 L = 1,000 mL | 1 hr = 60 min; 1 min = 60 s |
Worked examples
Worked example: Metric with a decimal
How many meters is $2.5$ km?
- Kilometers are bigger, so multiply by 1,000.
- $2.5 \times 1{,}000 = 2{,}500$: each digit moves three places left.
Answer: $2{,}500$ m
Worked example: Two steps
A 3 m ribbon is cut into pieces 25 cm long. How many pieces?
- Use one unit: $3$ m $= 300$ cm.
- Divide: $300 \div 25 = 12$.
Answer: 12 pieces
Worked example: Into a bigger unit
Six packages each weigh 12 ounces. How many pounds is that?
- Total: $6 \times 12 = 72$ ounces.
- 16 ounces make a pound: $72 \div 16 = 4\frac{8}{16} = 4\frac{1}{2}$.
Answer: $4\frac{1}{2}$ pounds
Common mistake
Mixing units, such as dividing 3 (meters) by 25 (centimeters). The numbers must count the same unit first. Check: a 3-meter ribbon is long, so there should be quite a few 25-centimeter pieces, not a fraction of one.