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
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Can anyone help me to find the answer step by step, please?
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?
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