转换单位

One of the most fundamental things you need to know in any science is how to convert between units.

You were probably told in elementary school that to convert $1000$ centimeters to meters, you need to divide $1000$ by $100$, because a centimeter is smaller than a meter. This method does work, but in the long run, it can become a disorganized way of converting units.

So, we are going to use something called the factor-label method. The idea behind this is we're going to multiply a quantity by a fraction, which, in theory, is equal to 1. This is best learned by example:

To convert $1000$ centimeters by meters, we multiply the quantity ($1000$ centimeters) by a conversion factor equal to 1:

$$(1000 \text{ cm})\left(\frac{1 \text{ m}}{100 \text{ cm}}\right) = 10 \text{ m}$$

In this method, we write the fraction such that we can cancel out some units that we do not need.

Another example:

Convert $235$ kilojoules to calories.

$$(235 \text{ kJ})\left(\frac{1000 \text{ J}}{1 \text{ kJ}}\right)\left(\frac{1 \text{ cal}}{4.18 \text{ J}}\right) = 56220 \text{ calories}$$

I've provided a unit conversion table as a reference.