To change units, multiply by conversion fractions, which equal 1 because the top and bottom are the same amount (like 5,280 ft over 1 mi). Write each so the unit you want to get rid of cancels.
Try it with your own problem ↓
The steps
- Write the starting amount as a fraction over 1.
- Multiply by a conversion fraction with the old unit on the bottom, so it cancels, and the new unit on the top.
- Repeat until only the unit you want is left.
- Multiply the tops, multiply the bottoms, and divide.
- Check the size: if you are converting to a smaller unit, the number should get bigger.
A worked example
Convert 60 miles per hour to feet per second.
- Write 60 mi/h. We need to change miles to feet and hours to seconds.
- Miles to feet: multiply by 5,280 ft / 1 mi. The miles cancel.
- Hours to seconds: 1 h = 60 min = 3,600 s. Multiply by 1 h / 3,600 s. The hours cancel.
- Now 60 × 5,280 × 1 / 3,600 = 316,800 / 3,600.
- 316,800 ÷ 3,600 = 88.
60 mph = 88 ft/s.
Common mistakes
- Putting the conversion fraction upside down. The unit you are leaving must end up in the denominator so it cancels.
- Mixing up multiplying and dividing. Let the units decide: if they cancel, it's right.
- Converting squared or cubed units like linear ones. 1 yd = 3 ft, but 1 yd² = 9 ft².
- Forgetting that temperature isn't just a factor. °F to °C needs subtract 32, then multiply by 5/9.
Questions people ask
How do I convert °F to °C?
Subtract 32, then multiply by 5/9. For 98.6 °F: 98.6 − 32 = 66.6, and 66.6 × 5/9 = 37 °C.
How many feet are in a mile?
5,280.
What is dimensional analysis?
The method on this page: keep the units in the calculation and cancel them, like numbers, to be sure you end up with the right one.
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