Learning goals
- Convert between units using multiply/divide by conversion factors
- Handle temperature conversions with the correct formulas (not simple scaling alone)
- Avoid inverted factors and mixed-unit mistakes
Think in conversion factors
Most unit conversions multiply or divide by a constant factor. If 1 inch = 2.54 cm, then inches → centimeters multiplies by 2.54, and centimeters → inches divides by 2.54 (or multiplies by 1/2.54).
Dimensional analysis helps: write the factor so unwanted units cancel. Starting in meters and multiplying by (100 cm / 1 m) cancels meters and leaves centimeters.
Temperature is the important exception. Celsius, Fahrenheit, and Kelvin are offset scales — you cannot convert °C to °F by multiplying by a single factor alone.
Linear unit conversion
new = old × (new units per 1 old unit)
Or new = old ÷ (old units per 1 new unit). Pick the orientation that cancels the unit you are leaving.
Celsius ↔ Fahrenheit
°F = (°C × 9/5) + 32 and °C = (°F − 32) × 5/9
Scale by 9/5 (or 5/9), then apply the 32° offset. Freezing is 0°C = 32°F; boiling is 100°C = 212°F.
Example 1 — Length: meters to feet
Given
Convert 2.5 m to feet. Use 1 m ≈ 3.28084 ft.
Steps
- Multiply by feet per meter: 2.5 × 3.28084 ≈ 8.2021.
- Round appropriately for the context (e.g. 8.20 ft for three significant figures).
Answer
2.5 m ≈ 8.20 ft.
Example 2 — Mass: pounds to kilograms
Given
Convert 180 lb to kg. Use 1 lb ≈ 0.453592 kg.
Steps
- Multiply: 180 × 0.453592 ≈ 81.6466 kg.
- Typical body-weight rounding: about 81.6 kg.
Answer
180 lb ≈ 81.6 kg.
Tip: Going the other way: kg × 2.20462 ≈ lb.
Example 3 — Temperature: °C to °F
Given
Convert 20°C to Fahrenheit.
Steps
- Multiply by 9/5: 20 × 1.8 = 36.
- Add 32: 36 + 32 = 68.
Answer
20°C = 68°F.
Tip: If you forget the +32, you get 36°F — a winter day — which is a useful sanity check that the offset matters.
Example 4 — Chained conversion
Given
Convert 3 km to inches. (1 km = 1000 m, 1 m ≈ 39.3701 in)
Steps
- 3 km = 3 × 1000 = 3000 m.
- 3000 × 39.3701 ≈ 118,110.3 in.
Answer
3 km ≈ 118,110 inches.
Inverting the factor
Common mistake
Converting cm → inches by multiplying by 2.54 instead of dividing.
Better approach
cm → in uses ÷ 2.54 (or × 0.3937). Ask: should the number get smaller when going to inches from centimeters? Yes for everyday lengths.
Treating temperature like length
Common mistake
“Double the Celsius” or multiply °C by 1.8 without adding 32.
Better approach
Always apply the full °F = (°C × 9/5) + 32 formula (or the inverse).
Check your understanding
1.Convert 10 cm to inches (÷ 2.54).
Answer: 10 ÷ 2.54 ≈ 3.94 in.
2.Convert 32°F to Celsius.
Answer: (32 − 32) × 5/9 = 0°C.
3.Convert 5 kg to pounds (× 2.20462).
Answer: ≈ 11.02 lb.
Key takeaways
- Most conversions multiply or divide by a factor so units cancel.
- Temperature needs scale and offset — not a single multiply alone.
- Sanity-check direction: should the numeric value grow or shrink?
- Chain conversions through SI (or another hub unit) when a direct factor is unknown.