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Math Help - Scale Ratio

  1. #1
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    Scale Ratio

    A map has a scale of 1:1000.
    (i) What distance on the ground (in meters) is represented on the map as
    (a) 2 cm (b) 7.6 cm

    (ii) What distance on the map represents
    (a) 100 m (b) 2.6 km

    ------------------
    Can anyone help me to find the answer step by step, please?
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  2. #2
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    Re: Scale Ratio

    Quote Originally Posted by joshuaa View Post
    A map has a scale of 1:1000.
    (i) What distance on the ground (in meters) is represented on the map as
    (a) 2 cm (b) 7.6 cm

    (ii) What distance on the map represents
    (a) 100 m (b) 2.6 km

    ------------------
    Can anyone help me to find the answer step by step, please?
    Normally the scale 1:1000 represents 1 cm : 1000 metres, now do the math...

    dokrbb
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  3. #3
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    Re: Scale Ratio

    Let me try (i)
    (a) 2 cm = 2000 m
    (b) 7.6 = 7600 m

    Are my answers correct?
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  4. #4
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    Re: Scale Ratio

    Quote Originally Posted by joshuaa View Post
    Let me try (i)
    (a) 2 cm = 2000 m
    (b) 7.6 = 7600 m

    Are my answers correct?
    seems to be

    Are you OK with the next part of the problem? How would you proceed?
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  5. #5
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    Re: Scale Ratio

    Since 1 cm on the map corresponds to 1000 cm of land, you are multiplying by 1000 to go from map to land. To go the opposite way, you have to do the opposite. What is the opposite of "multiply by 1000"?
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  6. #6
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    Re: Scale Ratio

    Quote Originally Posted by joshuaa View Post
    Let me try (i)
    (a) 2 cm = 2000 m
    (b) 7.6 = 7600 m

    Are my answers correct?
    You want to be careful with your units. The ratio 1:1000 is consistent with the fact that 1 cm on the paper is equivalent to 1000 cm on the ground. It's not a conversion factor, so 2 cm corresponds to 2000 cm. Unless the information says 1 cm = 1000 m (as the scaling ratio), I think it's a stretch to assume otherwise.

    What does everyone else think of this?
    Last edited by Lambin; April 15th 2013 at 12:25 PM.
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  7. #7
    Member dokrbb's Avatar
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    Re: Scale Ratio

    Quote Originally Posted by Lambin View Post
    You want to be careful with your units. The ratio 1:1000 is consistent with the fact that 1 cm on the paper is equivalent to 1000 cm on the ground. It's not a conversion factor, so 2 cm corresponds to 2000 cm.
    I suppose you meant metres, not cm
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  8. #8
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    Re: Scale Ratio

    Quote Originally Posted by Lambin View Post
    You want to be careful with your units. The ratio 1:1000 is consistent with the fact that 1 cm on the paper is equivalent to 1000 cm on the ground. It's not a conversion factor, so 2 cm corresponds to 2000 cm. Unless the information says 1 cm = 1000 m (as the scaling ratio), I think it's a stretch to assume otherwise.

    What does everyone else think of this?
    Quote Originally Posted by dokrbb View Post
    I suppose you meant metres, not cm
    No, I do mean centimeters. Because I could also say that 1:1000 implies 1 cm = 1000 km under the same assumption. The point is, only the map-creator would know what the conversion is exactly. So, with a ratio as 1:1000, the only safe assumption that can be made is that whatever measuring device you are using, the physical distance would be multiplied by 1000. Therefore, if it is 2 cm then it would 2000 cm. If it is 0.02 m then it would be 20 m. Both results would be consistent with each other because 2000 cm = 20 m and 2 cm = 0.02 m which is the same physical distance. Here, I'm illustrating that it doesn't matter what units we choose because the ratio is unitless.

    Disclaimer: I don't have much experience with maps, but to me, if we needed to know that 1:1000 is 1 cm = 1000 m, then you would need to know information beyond the text to be able to solve this problem.
    Last edited by Lambin; April 15th 2013 at 12:38 PM.
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  9. #9
    Member dokrbb's Avatar
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    Re: Scale Ratio

    Quote Originally Posted by Lambin View Post
    No, I do mean centimeters. Because I could also say that 1:1000 implies 1 cm = 1000 km under the same assumption. The point is, only the map-creator would know what the conversion is exactly. So, with a ratio as 1:1000, the only safe assumption that can be made is that whatever measuring device you are using, the physical distance would be multiplied by 1000. Therefore, if it is 2 cm then it would 2000 cm. If it is 0.02 m then it would be 20 m. Both results would be consistent with each other because 2000 cm = 20 m and 2 cm = 0.02 m which is the same physical distance. Here, I'm illustrating that it doesn't matter what units we choose because the ratio is unitless.

    Disclaimer: I don't have much experience with maps, but to me, if we needed to know that 1:1000 is 1 cm = 1000 m, then you would need to know information beyond the text to be able to solve this problem.
    for me is pretty obvious that 1:1000 couldn't be reffered to cm:cm since the real-life example "map" is given, and it's hard to imagine a practical usefullness of a map with a scale of 1 cm : 1000 cm,

    the second part of the problem also suggests to consider something else than cm in this ratio, and if this is not sufficiently convincing we can always consult http://http://en.wikipedia.org/wiki/Map_scale ,

    dokrbb
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  10. #10
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    Re: Scale Ratio

    Quote Originally Posted by dokrbb View Post
    for me is pretty obvious that 1:1000 couldn't be reffered to cm:cm since the real-life example "map" is given, and it's hard to imagine a practical usefullness of a map with a scale of 1 cm : 1000 cm,

    the second part of the problem also suggests to consider something else than cm in this ratio, and if this is not sufficiently convincing we can always consult http://http://en.wikipedia.org/wiki/Map_scale ,

    dokrbb
    I think that's a fair point, and it wouldn't be practical if it was a world map! But imagine if it was a museum map, then 1 cm : 1000 cm is plausible.
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  11. #11
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    Re: Scale Ratio

    Thanks to everyone who did give a useful information. I have really got the idea of how to solve the problem either Units where 1 cm : 1000 cm OR 1 cm : 1000 m.
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