How to Use Conversion Factors [Unit Conversions] скачать в хорошем качестве

How to Use Conversion Factors [Unit Conversions]

In this video I go over how to use conversion factors and how to perform any unit conversion while going over a few good examples for demonstrating how this is done. Converting units with conversion factors are important to solving problems in math, physics, chemistry, biology, and engineering. Knowing how to convert units with conversion factors can be very easy and performing dimensional analysis is a powerful tool for solving problems and checking answers. The first step in converting using is to find a conversion factor. A conversion factor is what connects the unit you have to the unit you want. When you have a relationship between units, such as 1 km = 1000 m, this can be made into a conversion factor by dividing one side by the other. There are two possible conversion factors, (1 km / 1000 m) or (1000 m / 1 km). To figure out which one we should use, we choose the factor that will cause the unit we have to cancel, one in the numerator and one in the denominator, and the unit leftover should be where we want it. Sometimes conversion factors can easily be found to take you straight from the unit you have to the unit you want, but sometimes it is easier to break the conversion into multiple steps. This tends to be true when converting from British units to SI units, or the metric system. Then we can simply chain together conversions where all of the units in intermediate steps will cancel, and we're left with what we want. Conversion factors work because they are all equal to 1. This is because we took two things that are equal and divided one by the other. Anything divided by itself is 1. Then we take the conversion factors and multiply by them. Since we're multiplying by 1, we're not changing the quantity we have. We're simply expressing it in different units which is our goal. Converting units that have exponents such as m^3 to mm^3 tend to give people problems. To convert these units, we start begin by ignoring the exponent and focus on the base unit. In this case, we would create a conversion factor form m (meters) to mm (millimeters). Then once we have our conversion factor which equals 1, then we raise it to our exponent. Raising 1 to any exponent will give use 1, so we're still not changing our quantity, we're just converting it. It's useful to to put the conversion factor in parentheses and then raise it to the desired exponent. If you want to carry the exponent inside the parentheses, remember it will apply to every number and every unit. Dimensional analysis is the process of looking at units and making sure they match what you expect. For example, velocity and speed have units for length divided by time^2. So the units should match the dimensions. The unit in the numerator should be a unit for length, such as meters, miles, feet, etc., and the denominator should have units of time squared, such as seconds^2 (s^2) or hours^2 (h^2). Noticing that the units do not match, let's you know there is a mistake somewhere. In performing dimensional analysis, we should realize that we can perform mathematical operations with units. Multiplying meters by meters gives meters squared ( m * m = m^2 ). Dividing kilograms squared by kilograms gives kilograms ( kg^2 / kg = kg ). A math operation that can be confusing is addition and subtraction. We can only add or subtract units with the same units, and doing this gives us back that same unit. For examples, if we add a second to a second, we'll get some amount of seconds. Also, if we subtract a second from a second, the answer does not cancel and go away! Subtracting some number of seconds from another number of seconds, will leave us with some number of seconds, even if that is 0 seconds. So ( seconds - seconds = seconds ) when working with units because there are actually some numbers in front of our units.