In order to be able to compare distances, it is important that the lengths be in the same units. There are several famous examples of unit conversion mistakes that have led to disasters, such as the metric conversion disaster that resulted in a NASA orbiter drifting off-course. Therefore, understanding unit conversion and how to check one's work can help reduce frustrating errors or even potential disasters!
How to Convert Inches to Centimeters
Inches and centimeters (sometimes abbreviated to cm) are both units of length. They sound similar in scale, but 1 inch is equal to 2.54 centimeters. If one needs a very quick estimate of how many centimeters are equivalent to some length in inches, multiplying the number of inches by 2.5 is a good way to get a rough estimate of the length without using a calculator.
Remember that an inch is longer than a centimeter. Therefore, if you cannot remember whether to multiply or divide by the conversion factor, try one and see if there are there more centimeters in the result for the given number of inches (or vice-versa).
For example, if you are converting 10 inches to centimeters and end up with 4 cm, you can double-check by noticing that the number of centimeters is less than the number of inches. Because a centimeter is shorter than an inch, it takes more centimeters to cover the same distance. Therefore, you can quickly re-evaluate the conversion, use a different operation and determine that there are 25.4 centimeters in 10 inches.
The General Concept of Unit Conversion
In order to convert one unit to another, we need to be able to transform the quantity into another unit without changing the quantity represented. Therefore, knowing the conversion factor between two units is critical. For example, there are 12 inches in 1 foot, and 100 centimeters in 1 meter; therefore, the conversion factors would be 12 inches = 1 foot and 100 centimeters = 1 meter.
The reason knowing the conversion factor is the most important, is because it is a form of the number 1; multiplying a number by 1 does not change the quantity. In the case of conversion, the conversion factor is the multiplicative factor that equals one.
Conversion With Metric Prefixes
We have already covered the inch-to-cm conversion: 1 inch equals 2.54 cm. Using the formula above, one can now use the conversion factor to quickly convert inches to centimeters.
However, quite often quantities in the metric system are described by prefixes which are used to signify the order of magnitude of the number; for example, millimeters, microseconds and picograms. The standard in each of the previous examples is meters, seconds and grams respectively, and the prefix allows us to specify the order of magnitude faster.
For example, many rulers also subdivide centimeters into millimeters (often abbreviated mm). The centi- prefix refers to the fact that there are 100 centimeters in one meter, and the milli- prefix refers to the fact that there are 1,000 millimeters in one meter. The mm-to-cm conversion is therefore, 10 mm = 1 cm.
The prefix system does not work in imperial units, in which case small quantities are often rewritten in scientific notation, for ease of use.