How many millimeters are there in 0.55 kilometers?
It’s not often that we need to convert a length in kilometers into millimeters. So let’s start by reminding ourselves what different units of length are worth. Firstly, we know that one kilometers is equal to 1000 meters. And we’re going to need to use this fact to help us. But what’s one of those meters worth? One meter is the same as 100 centimeters. And what’s one of those centimeters worth? One centimeter is equal to 10 millimeters. The first thing we can do with these facts is to find out how many millimeters there are in one kilometer. And we can use this to help us find out how many millimeters there are in 0.55 kilometers. As we’ve said already, one meter is equal to 100 centimeters.
And another of our facts has told us that each of our centimeters is worth 10 millimeters. So to calculate the number of millimeters in a meter, we need to multiply the number of centimeters, which is 100 by 10. 10 times 100 equals 1000. There are 1000 millimetres in a meter. Let’s change our bar model slightly. This time we’re thinking about one kilometer. We know from the facts we discussed earlier on that one kilometer is the same as 1000 meters. And as we’ve just found out, each of those meters is worth 1000 millimetres. So the number of millimeters in one kilometer is worth 1000 lots of 1000.
Here’s what 1000 looks like on a place value grid. And when we multiply this number by 1000, the digits move three places to the left. So let’s see how this number changes as we shift it three places to the left. One — and we need to draw an extra zero in the ones place to show that we’ve shifted it one place to the left — two, three. 1000 lots of 1000 equals one million. So one kilometer is worth 1000 meters or one million millimeters. So to find out how many millimeters there are in 0.55 kilometers, we need to multiply 0.55 by one million.
We’re going to need another place value grid to help us do this, this time one that involves tenths and hundredths. Let’s write our number of kilometers on there, 0.55. So we need to multiply this number by one million. As we’ve said already, one million is 1000 thousands. And if we multiply by 1000, we move the digits three places to the left. So if we want to multiply by 1000 thousands, we need to multiply the digits six places to the left. A nice way of remembering this is to look at the number one million and see that there are six zeros. This remind us that we can move the digits six places.
So let’s move our digits six places to the left. One, two, three. So far, we’ve moved the digits three places. That’s the same as multiplying by 1000. 1000 lots of 0.55 is 550. Let’s keep multiplying. So far we’ve shifted the digits three places, four, five, six. We multiplied 0.55 by one million by shifting the digits six places to the left. 0.55 multiplied by one million equals 550000. And so we know 0.55 kilometers is the same as 550000 millimetres.