In this video, we’re going to learn about unit conversions, what they are, why they’re important, and how to do them practically.
To start off, let’s imagine that a friend of yours, a true lover of ice cream, one day decides to try to set the world record for fastest ice cream scooping. Reading up a bit on the topic, you both find out that the current world record for speed ice cream scooping is 4.08 kilograms of ice cream scooped in one minute of time. So, you grab a stopwatch. And with you keeping time, your friend sets out to try to beat that world record.
After one minute of time has elapsed, you check the three-gallon containers that your friend has been furiously scooping ice cream out of. Two of the containers are completely empty. And the third is untouched, full. You know that each gallon holds five pounds of ice cream. So, your friend in 60 seconds has scooped a total of 10 pounds, that is, 10 pounds of ice cream in one minute of time. And the question is, is this amount of ice cream scooped greater than, equal to, or less than the current world record? To find out, it will be necessary to perform a unit conversion.
We can define unit conversion as exchanging a value expressed in one measurement unit to a value expressed in another, without changing the absolute measured amount. For example, one fortnight, which is a length of time, is equal to 14 days. So, we could express an interval of 14 days as 14 days or one fortnight. Either way, we haven’t changed the absolute measured amount of time passed. It’s an example of converting this measured value of time from one unit to another.
In general, a conversion factor is all we need to convert from one set of units to another. One fortnight being equal to 14 days is an example of a conversion factor. Unit conversion is something that comes up fairly often when solving physics exercises. And we might wonder why this would be. Unit conversion is so common largely because there are many different measurement systems across the world. If we want to be able to communicate across these different systems, unit conversion is needed.
Just think, for example, of all the different units that we use to measure distance. We measure distance in centimeters. We measure it in furlongs. We measure it in angstroms. We measure it in fathoms. We measure it in feet, lunar distance, chains, rods, Planck lengths, and more. To connect all these different ways of measuring distance with one another, we use unit conversions. Let’s get some practice using unit conversions now.
One fluid ounce is equal to approximately 30 milliliters. A can of soda pop has a volume of 12 fluid ounces. What is the volume of a can of soda pop in cubic meters?
We want to solve for the volume, we’ll call it capital 𝑉, of a can of soda pop in cubic meters. We’re told that one fluid ounce is approximately 30 milliliters and that a can of soda pop has a volume of 12 fluid ounces. What we want to do then is take our volume of 12 fluid ounces and convert it to some number of cubic meters.
So, we begin with our initial given volume, 12 fluid ounces. We’re told that one fluid ounce was equal to 30 milliliters. So, if we multiply our given volume by that conversion factor, 30 milliliters per one fluid ounce, then we see, when we multiply these two numbers together, the units of fluid ounces cancels out. And we’re left with units of milliliters.
That’s a good start. But we want our final answer 𝑉 in terms of units of cubic meters. So, now we seek for the conversion factor between liters and cubic meters. We find that one liter is equal to 0.001 meters cubed. Or one milliliter is equal to one times 10 to the negative sixth cubic meters. When we multiply our fraction by this conversion ratio, we see that the units of milliliters appear in the numerator and denominator. So, as we multiply it through, they cancel out just like fluid ounces did.
We’re left with a result in units of cubic meters, which is what we were seeking for. To find the value, the actual volume, we only need now to multiply these three fractions together. When we do, we find a volume of 3.6 times 10 to the negative fourth cubic meters. That’s the volume of a can of soda pop expressed in cubic meters. Let’s try another exercise involving units conversion.
The speed limit on some interstate highways is roughly 100 kilometers per hour. What is this in meters per second? How many miles per hour is this? Note, one mile equals 1.6 kilometers.
First, we’ll solve for this speed written not in kilometers per hour as it’s given but in meters per second. To do that, we’ll first write out our given speed as a fraction. Currently, this fraction has distance units of kilometers and time units of hours. And we want to change those to meters and seconds, respectively. When we recall or look up the unit conversions for those distances and times, we find that one kilometer is equal to 1000 meters and one hour is equal to 3600 seconds. Now, what we’ll do is we’ll take these two conversion factors and apply them to our given information.
First, we’ll multiply our 100 kilometers per hour by a conversion factor from kilometers to meters. Notice that if we perform this multiplication, our units of kilometers cancel out. Next, we multiply by our unit conversion from hours to seconds. Notice again that our units of hours, our unwanted time unit, cancel out. And we’re left in this fraction with units of meters and seconds just as we wanted. When we multiply these three fractions together, we find a result of 27.8 meters per second. That’s a speed of 100 kilometers per hour converted to units of meters per second.
Next, we move on to expressing our initially given speed in kilometers per hour to a speed in miles per hour. And we’re told that one mile is equal to 1.6 kilometers. Once again, we write out our given speed as a fraction. And using the conversion factor we’re given in the problem statement, multiply it by it, so that we can see that units of kilometers cancel as distance. And we’re left with distance units of miles divided by time units of hours. When we multiply these two fractions together, we find a result of 62.5 miles per hour. That’s the speed limit expressed in those units.
Now, let’s go back to our ice cream scooping record attempt. We know the world record currently for scooping ice cream is 4.08 kilograms in 60 seconds. Our friend scooped 10 pounds of ice cream in one minute. And we’d like to convert that amount to kilograms per minute to figure out where we stand.
We look up the conversion factor and find that one kilogram equals 2.2 pounds. So, if we take our fraction, 10 pounds per minute, and multiply it by this conversion factor, we see the units of pounds cancels out. And we’re left with units of kilograms for our mass. When we multiply these two fractions together, we find that our friend scooped 4.55 kilograms of ice cream in one minute. That’s a new world record.
So, in summary, unit conversion is exchanging a value expressed in one measurement unit to a value expressed in another, without changing the absolute measured amount. Unit conversion allows communication across different unit systems. And memorizing common conversions, not all of them, is helpful in speeding up problem-solving.