Math Checkup: Converting Linear Measurements in Imperial and Metric
When doing unit conversion, 4 basic facts must be memorized:
| 1000 mm = 1 m |
| 25.4 mm = 1 in |
| 12 in = 1 ft |
| 3 ft = 1 yd |
The classic problem when doing unit conversions is, “do I multiply or divide.” There is a simple rule that may help you figure it out.
| Small -> Large -> Small | When converting from a smaller unit to a larger unit, the answer must be smaller than what you started with. | Divide* |
| Large -> Small -> Large | When converting from a larger unit to a smaller unit, the answer must be larger than what you started with. | Multiply* |
*Note: This is not always true, but if you use the unit conversion above, it will always work. For example, dividing a number by something between 0 and 1 will make the number larger.
Example Convert Millimetres to Inches:
Millimetres are a smaller unit than inches, so the rule is “small => large => small”. Use division to make 758 smaller. The conversion factor is 25.4 because there are 25.4 millimetres in one inch.
Example Convert Yards to Feet:
Yards are a larger unit than feet. The rule is “large => small => large”. The answer needs to be larger than 4.79 so use multiplication. The conversion factor is 3 because there are 3 feet in one yard.
Doing Unit Conversions in Multiple Steps
In some cases, you may need to do unit conversions that take several steps. For example, how many millimetres are there in a foot? If you don’t have this memorized that’s ok because we know how many millimetres in an inch, and then how many inches there are in one foot.
Example Convert Millimetres to Feet
Convert 2378 mm to inches.
This can be done in one step in your calculator:
One way to navigate through several steps of unit conversions is to use this visual. Keep in mind, this isn’t something that is available to you on your test. Use it to start your practice, but you need to be confident enough to go without it.
Going from left to right (top red) follow the multiply and divide signs on top. Going from right to left (bottom blue) follow the multiply and divide signs on the bottom. The conversion factors are written in green between the units.
Example Convert Millimetres to Feet Revisited
Start from millimetres, move to the right across inches to feet. Look at the top to see you divide by 25.4 and by 12.
