Scale Drawing/Ratio

1. Sep 6, 2006

petuniac

I have a problem that shows a picture with an arrow in it. The arrow in the picture shows that is is 5 cm in length. The actual length of the arrow is given in the problem as 43 m. The question asks for me to determine the scale of the picture.

So, I've set up a ratio:

1/x = 5/45 (1 cm in picture/x m acutal = 5 cm in picture/43 m actual)

I solve and get the scale to be 1:8.6

I think that I have the right idea, but the solution should be 1:86. Am I supposed to get rid of the decimal in the final answer??

2. Sep 6, 2006

Integral

Staff Emeritus
How many meters is 5cm?

3. Sep 6, 2006

petuniac

5 cm = 0.05 m which then gives an answer of 860, which is still the wrong answer and i was under the impression that the units did not need to be convered as this was a ratio?

4. Sep 7, 2006

HallsofIvy

Staff Emeritus
Where did you get that impression? A ratio does not have units because they cancel out- in order to do that, the units in numerator and denominator have to be the same. It doesn't matter if they are meters or feet or kilograms, but they have to be the same.

"1/x = 5/45 (1 cm in picture/x m actual = 5 cm in picture/43 m actual)"
should be 1/x= 0.05 m/43m so x= 43/0.05= 860 or 1/x= 5 cm/4300 cm so
x= 4300/5= 860. 860 is correct, not 86.
(As a quick check: 100 time 5 cm is 5 m. To get to 43 m, the ratio must be much larger than 100.)