Converting map scales

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Probability

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This could just be me not seeing it but also could be a clerical error!

The example says, convert 250 000 cm to kilometers.

Now,

250 000 cm = (250 000 divided by 100) m = 2500 m

(2500 divided by 1000) km = 2.5 km

Where is the problem?

There are 100 cm in a metre. There are 1 thousand millimeters in a metre. I'd of thought it should have said;

250 000 cm = (250 000 divided by 100) cm = 2500 cm

Now 100 cm = 1000 millimeters, therefore;

(2500 divided by 1000) km = 2.5 km

so the map scale would read; 1 cm represents 2.5 km.

Am I over complicating this or is there a genuine error?
 
Probability said:
This could just be me not seeing it but also could be a clerical error!

The example says, convert 250 000 cm to kilometers.

Now,

250 000 cm = (250 000 divided by 100) m = 2500 m

(2500 divided by 1000) km = 2.5 km

Where is the problem?

There are 100 cm in a metre. There are 1 thousand millimeters in a metre. I'd of thought it should have said;

250 000 cm = (250 000 divided by 100) cm = 2500 cm

Now 100 cm = 1000 millimeters, therefore;

(2500 divided by 1000) km = 2.5 km

so the map scale would read; 1 cm represents 2.5 km.

Am I over complicating this or is there a genuine error?
Click to expand...
It isn't clear what the problem itself said, what the source gave as the answer, or what you are saying it should be.

If the problem you are working on was, "convert 250 000 cm to kilometers", that has nothing to do with map scales! The answer would be 2.5 km; that is, 250 000 cm = 2.5 km. This is entirely different from "1 cm represents 2.5 km".

Also, I see nothing in the problem about millimeters, so I don't know where that came from.

And how could you imagine that "250 000 cm = ... = 2500 cm"? Those are clearly different lengths.

I hope I am just misinterpreting what you are saying. If so, please clearly state the problem, the answer you disagree with, and the answer you think is correct.
 
Sorry it is all down to my interpretation, which I have misunderstood.

I could see that;

250 000 cm = (250 000 divided by 100) m = 2500 m

I can see that there is 1000 mm in a metre, hence

(2500 divided by 1000) km = 2.5 km

So the map scale is 1 cm (on the map) represents 2.5 km on the road.

Really that was not my concern, the confusion was all mine in the way I misinterpreted (250 000 divided by 100) m

(100) I took to be meaning 100 cm, or I thought it should have said 'cm' instead of 'm', however even though I knew 100 cm is equal to 1 metre, the bold section (100) m confused me, hence asking for advice. It is however correct it just throw me off in the interpretation.
 
Why have you not answered my questions, by stating the actual problem, and leaving me to continue guessing??? There is a reason we ask you to state the entire problem as given to you.

Probability said:
Sorry it is all down to my interpretation, which I have misunderstood.

I could see that;

250 000 cm = (250 000 divided by 100) m = 2500 m

I can see that there is 1000 mm in a metre, hence

(2500 divided by 1000) km = 2.5 km

So the map scale is 1 cm (on the map) represents 2.5 km on the road.

Really that was not my concern, the confusion was all mine in the way I misinterpreted (250 000 divided by 100) m

(100) I took to be meaning 100 cm, or I thought it should have said 'cm' instead of 'm', however even though I knew 100 cm is equal to 1 metre, the bold section (100) m confused me, hence asking for advice. It is however correct it just throw me off in the interpretation.
Click to expand...
Surely here you must have meant 1000 m in a kilometer, since as I already pointed out, there are no millimeters elsewhere in all you've written!

And here, nothing you have said is about a map scale, and what has been shown is about 250 000 cm, not about 1 cm. It appears that the real problem, WHICH YOU HAVE NEVER STATED!, has to do with a map scale of 1 : 250 000, so that 1 cm on the map represents 250 000 cm = 2,5 km in the world. That is correct.

As for the way the work is shown, I wouldn't write it that way. But when they (as I am guessing) said

250 000 cm = (250 000 divided by 100) m = 2500 m​

they are just saying that the number of meters is 1/100 of the number of centimeters. The "m" is not attached to the 100, but to the entire parenthesized expression.

For clarity, I would do this:

[MATH]250 000\text{ cm }= 250 000\text{ cm }\times\frac{1\text{ m }}{100\text{ cm }} = \frac{250 000}{100}\text{ m } = 2500\text{ m }[/MATH]​

This makes it clear that the conversion is based on the fact that 1 m = 100 cm.
 
I'm sorry for all the confusion I seem to be creating. There is no math problem, it was however my interpretation of 250 000 cm (250 000 divided by 100) m.

That was the whole problem.

I was told to convert 250 000 cm to kilometers. This is a map problem converting distances from the map to the actual roads.

Everything became unclear at 250 000 cm (250 000 divided by 100) m

I could not get my head round why the author had said 250 000 cm and then used 100 with an 'm' outside the bracket, which mislead me to think a typo or something had occurred because I understood the 100 to be 100 cm and not meters. What was added to the confusion was the fact that the 250 000 had 'cm' at the end. map scale factors don't have units at the end, they just read as 250 000 or 1:250 000.

As you pointed out earlier it is easy to say map to ground multiply by scale factor, and ground to map divided by scale factor, but I think the author wants the student to understand from first principles how to convert the units from 'cm', m and km. I just think now that the material could have made it more clear about unit conversions before this topic, and maybe given a few examples.
 
Maybe we're just using the word "problem" differently. You say "there is no math problem", and "the whole problem" was the conversion; but then you say, "This is a map problem". To me, "the problem" is whatever you are working on, which evidently is something about reading a map. Are you partly using the word "problem" to mean "difficulty"? And there is some author of something who said something you didn't understand, but I don't know what he is writing about.

"Convert 250 000 cm to kilometers" is not a map problem. It is apparently part of the work of solving a problem involving a map. I could probably explain things better if I only knew what you are actually told about the map.

Anyway, the "100" is not 100 cm or 100 m, but really 100 cm per meter. That's the conversion factor for units.

Please, please, tell me what the actual map problem was. Are you saying it said "1 cm : 250 000 cm", or what?? If it's online, give me a link; if it's in a book, attach a picture if you can. But as it is, I just don't know what was said that you are commenting on. I can't tell you if it's unclear without seeing it all, from start to finish, not just the one line you quote out of context.

Or, we can just drop it, since you seem to be sort of satisfied with your understanding.
 
Thanks Dr Peter. We'll drop it now I understand my confusion. More important things to move onto.
 
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