Mass is concept that requires some heavy thinking. There are actually at least seven different definitions of mass used in physics today. But since this is a math site, and not a physics or chemistry site, and this chapter is about everyday math, we will talk about the units related to the concept of mass as we use it in our day-to-day lives. Which is not actually the concept of mass, but the concept of weight.
What’s the difference? Well, gravity. A body has a certain mass whether there is or there isn’t any gravity present. It is an intrinsic property of that body. But weight is not an intrinsic property of said body because there has to be gravity present for it to have any weight. Also, weight depends on the strength of the gravitational field – you don’t weigh as much on the surface of the Earth and in deep space.
So, when we use scales for measurement, they are not actually showing us the mass of the object we are weighing. But, since the scales are calibrated for the strength of the gravitational pull of the Earth on its surface, we can continue to use them interchangeably in our daily lives without fear of a major error. It also means we can use the same units to express mass and weight, and the SI unit for mass is a kilogram.
The kilogram is defined using the “international prototype kilogram”, a physical object internationally recognized as weighing exactly one kilogram. It is a metal cylinder, made from a platinum-iridium alloy which is (by mass) 90% platinum and 10% iridium. It is kept in Sèvres, France, and copies of it are kept all over the world. In the table below, we can see the various SI multiples from gram (g).
Are there other units we can use for expressing mass? Well, yes, there is an abundance of them. A kilogram is an SI unit, and it is used wherever people use the metric system. But, depending on the definition of mass, the system of measurements we use, and the weights and measures we have at our disposal, we can use a large number of seemingly unrelated units.
Let’s look at the imperial system of units. In the table below, we can see the different units used even today to express mass and weight in the United States of America and in the United Kingdom.
Using these units, we can easily compare the weights of different objects. To do that, we must reduce their weights to the same unit. When we do that, we can compare weights, add them up, and perform all kinds of mathematical operations with them.