Metric system unit conversion examples

Tomas dropped off two packages to be shipped. One package weighed 1.38 kg and the other package weighed 720 g. So the first one they given in kilograms and the second one they give us in grams. What was the combined weight of both packages in grams?

So what I want to do is I'm going to convert both of these to grams and then add them up to get the combined weight. Well, we already know the second one is 720 g, but what's the first one in terms of grams? Well, let's see. 1.38, I could write kilogram like that. Well, if 1 kilogram is 1,000 g and that's what the prefix kilo means— it means a thousand.

Well, to go from 1 to 1.38, I'm multiplying by 1.38. So I'm also, if I wanted in terms of grams, I would take 1,000 g and multiply by 1.38. So this is going to be 1,000 * 1.38 is 1,380 g, which I could have just denoted with a g.

But now let's add those together. This is the first package, and then the second package is 720 g. So if I were to add this— let's see, got a zero; 10, that's let's see, 4 + 7 is 11, and then 1 + 1 is 2— we get 2,100 g in total.

Let's do another one of these unit conversion examples. Julia and her friends are making kites out of paper. For each kite, they need a piece of paper that is 0.65 m wide. How many cm of paper will they need to make four kites?

So they tell us how wide the paper is in meters for each kite, but they want the answer in centimeters and they want it for four kites. So let's think about this a little bit. Each kite is 0.65 m, 0.65 m. So to go from 1 to 0.65, you multiply by 0.65 on the meters.

And so to go to 100 centimeters to the number of centimeters you would need for the width of a kite, you'd similarly multiply by 0.65. Well, 0.65 * 100 is going to be 65 cm per kite. So this 0.65 m wide per kite in centimeters is 65 cm.

Now they don't want just how much paper will they need to make one kite; they want four kites. So we would multiply this by 4. This is how much we need per kite. So let's multiply that times four, and so let's see: 4 * 5 is 20, 4 * 6 is 24 + 2 is 26— 260 cm of paper for the width of the four kites.

Let's do one more of these; this is a volume conversion. Omar is pouring 5 L of water into two goldfish bowls. He spills 200 milliliters of water and then divides the remaining water evenly between the two bowls. How many milliliters of water does Omar pour into each bowl?

So we want our answer at the end in milliliters. And so let's just convert the amount that he starts with into milliliters. So he starts with 5 liters. So how many milliliters is that going to be? Well, they tell us 1 liter is 1,000 milliliters. So if we have 5 liters, so we're multiplying our quantity times 5; it's going to be five times as many milliliters. So that's 5 * 1,000 = 5,000 milliliters.

So that's what he starts with. Now, before he splits this 5,000 milliliters between these two bowls, he spills 200 milliliters. So let's subtract out what he spills because that's not going to be able to be split.

And so that's going to give us— so we're going to have 4,800 milliliters to split between those two bowls. And so each bowl—that's what they ask us: how many milliliters of water does he pour into each bowl? Well, if he's going to split this into two bowls, each bowl is going to get half of this.

So each bowl is going to get half of 4,800. So we just divide that by two. So each bowl is going to get 2,400 milliliters. 2,400 mL, and 2,400 mL— that's how much each bowl is going— that's how much Omar is going to pour into each bowl.