How to Calculate the Ratio Between Two Numbers

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Suppose someone told you that every inch of rain equals 13 inches of snow, on average, in the United States. (This is true using at least one reliable data set, but the amount of snow per inch of rain can be as little as 2 inches in the case of sleet and as much as 50 inches in the case of light powder snow.) This means that if it's cold enough, what would have been 1 inch of rain per the weather forecast is 13 inches of fresh snow outside your window.

But what if the amount of snow is different, say, a whopper of a storm dropping 26 inches on your town? Could you then determine how much rain this could have been in warmer conditions? That is, if you already know that 1 of x means 13 of y (or some other combination of numbers), can you expand this to mean that given any value for either x or y, you can figure out the other one?

What Is a Ratio?

The answer to the above question is yes, and this is where the concept of the ratio between two numbers becomes a part of your mathematical skill set — even if you have no plans to become either a skier or a meteorologist.

A ratio is a kind a fraction, one whole number (... -3, -2, -1, 0, 1, 2, 3 ...) "over" another. This is the same basic operator as division, so a ratio is also a quotient. Examples are 1/3 and 8,298/27,209.

From "Ratio-Like" to Ratio

The number 10.2/34 is not a ratio, because the numerator (the top number) is a decimal number. The way to convert this number into a ratio is to multiply the numerator and the denominator (bottom number) by the correct power of ten to eliminate the decimal point. In this case, (10)[10.2/34] = 102/340, which is a ratio.

This ratio can be simplified to 3/10 by dividing both the numerator and the denominator by the largest common factor of each, which is the biggest number that fits an even number of times into both. In this case, this number is 34. But generally you do not have to simplify ratios unless asked to do so. (Also, dividing 10.2 by 34 gives the decimal number 0.3, which you may immediately recognize as the ratio 3/10.)

Ratio Examples

In a number of famous traditional stories passed down through various cultures, the world at some point has been besieged with colossal, even devastating amounts of rainfall. Suppose that over 3 feet of rain was in your area, and a neighbor demanded that you convert 40 inches of rain to snow in case it became colder than expected before precipitation got underway.

Based on the above discussions, you know that "1 is to 13 as x is to y" is solvable as long as you have either x or y. You don't need a special ratio calculator; just set up a proportion:

(1" of rain/13" of snow) = (40" of rain / y inches of snow)

1/13 = 40/y; (40)(13)/1 = y = 520"

"520 inches of snow would be how many feet?" should be your first question after obtaining this eye-opening total, and the answer is (520/12) = 43.333... , or 43 feet, 4 inches. That would be enough for a few days off from school for sure!

Snow Accumulation Calculator

Online, you will find websites that do some easy calculations back and forth between rain and a couple of different kinds of snow. Note that some sources use slightly different numbers than described above; snow-to-rain conversions depend on temperature and other factors and are always intended as reasonable expectations and nothing more.

References

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.