Writing scales with and without units
About this video
A scale can be written without units only after both parts are in the same unit. The video turns 1 mm to 7 cm into 1 to 70, and then goes the other way, turning 1 to 475 into 1 cm to 4.75 m.
You'll be able to
- rewrite a scale with units as a scale without units.
- rewrite a scale without units as a scale with given units.
- convert between millimeters, centimeters and meters.
Key words
- scale
- A rule that tells how a length on a drawing matches a real length.
- scale without units
- A scale written as just numbers, like 1 to 70, where both parts are in the same unit.
- millimeter
- A small unit of length; 10 millimeters make 1 centimeter.
Transcript
- [Narrator] We're told a drawing uses a scale of one millimeter to seven centimeters. Rewrite the drawing scale without units. And they start us off, it says one to, something. And we just wanna put a number here. So pause this video, and have a go at that. All right, now let's do this together.
When you first look at this, you're like, oh, it looks like there's a one and a seven. Maybe this is one to seven. But these aren't the same units. If this said one millimeter to seven millimeters, then it would be one to seven. But these aren't the same thing.
So in order to do this, we'd want to convert them to the same units. And for simplicity, let's just convert the centimeters to millimeters. One centimeter has how many millimeters? Let me write this down. One centimeter is equal to how many millimeters? Well, it's equal to 10 millimeters.
One way to think about it is a hundred of these make a meter, a thousand of these. So you're going to have one centimeter is equal to 10 millimeters, or seven centimeters is the same thing as 70 millimeters. So the drawing scale is actually one to 70 when we get to the same units.
Let's do another example. But in this one we're going to go the other way around. We're told the scale. A map has a scale of one to 475, but now they want us to write the scale with units. So it's one centimeter to how many meters? So pause this video again and have a go at this.
Well, if we kept everything in centimeters, we could write it as one centimeter to 475, 475 centimeters. But they don't want this. They want us to give 475 centimeters in meters. So how do we convert that? Well, one way to think about it is you have 100 centimeters per every one meter, or you could say a meter is equal to 100 centimeters.
So what you wanna do is actually divide this by 100. Another way you could think about it, if you really want to think about units, 475 centimeters x 1 meter for every 100 centimeters. And you can think of it as these units are canceling out. And so you'd have 475 x 1 divided by 100 meters.
So you'd have 475 over 100 meters, which is the same thing as 4.75 meters. So one centimeter to 4.75 meters.
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