Ratios Containing a Zero
Date: 07/03/2005 at 21:27:57 From: Jackie Subject: Ratios with 0 in them What does the ratio 1:0 mean? What does the ratio 0:1 mean? What does the ratio 0:0 mean? Are they meaningless like dividing by 0? I am having trouble understanding whether they exist or are meaningless and disallowed? Please help. 1:2 means that, for example, for every 1 cm on a map, it represents 2 cm. Therefore, a ratio of 1:0 means that for every 1cm on a map, it represents nothing. Also, a ratio of 0:1 means that for every 0 cm on a map, it represents 1 cm. Both of those ratios are impossible. But are they meaningless?
Date: 07/03/2005 at 23:28:48 From: Doctor Peterson Subject: Re: Ratios with 0 in them Hi, Jackie. I think you've got the right idea. I wouldn't actually say that these ratios are meaningless--they do mean something!--but for many purposes such a ratio means that something is useless. The ratios themselves are not meaningless, but in a specific application they may be invalid. The ratio 0:1 means that the first item will be zero no matter what the second is; for example, your map would have no size at all. So you will never find a map with that scale. Similarly, a ratio of 1:0 would mean that the map showed nothing. Ratios often are turned into fractions; 0:1 becomes 0/1, which is the perfectly respectable value 0, while 1:0 becomes 1/0, which is undefined (though in some situations you can think of it as "infinite"). One benefit of ratios is that both 0:1 and 1:0 are meaningful, whereas 1/0 is not defined. If, for example, they represent the ratio of blue to white paint in a mixture, the first means pure white, and the second means pure blue. Both ratios are perfectly fine in that setting! If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 07/11/2005 at 01:42:53 From: Jackie Subject: Thank you (Ratios with 0 in them) Thanks for making me understand where those ratios may be used.
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.