Variations in Rounding

rulersIt turns every math problem involving inches and feet into a lesson in conversion.

It's not just the whole converting-inches-into-feet confusion. It even extends to the dilemma over decimals. Is an object that is 2 feet 6 inches, 2.6 feet? No that would be 2.5. As in 2 1/2.

This is all in sharp contrast to the wonderfully simple metric system, which of course is a base ten number system. For example, it is a breeze to convert 4.32 meters to 432 centimeters.

How should we express the inches part of the measurement?
The easiest way is to express the inches part of the measurement as a fractional number of feet. You divide by 12, since there are 12 inches/foot. So 3 inches is 3/12 foot and 8 inches is 8/12 foot. Use a calculator if you want and express the fractions as decimals.

rulers2For example: 3/12 = 0.25 and 8/12 = 0.67 (rounded to two decimal points). So 12 feet 3 inches is 12.25 feet, and 15 feet 8 inches is 15.67 feet. Multiply these numbers with a calculator and get an answer of 191.96 square feet, approximately.

Isn't there an easier way?
Depending on the application, a rough estimate might be OK. Round the measurements to the nearest square foot. That is, round down any measurement that has an inches part less than 6 and round up any measurement that has an inches part more than 6. So, round 12 feet 3 inches to 12 feet and round 15 feet 8 inches to 16 feet. Multiply 12 times 16 to get 192 square feet. That's very close to the true answer in this case. (And it's so much easier.)

PDROM Bar Video

bithell students3 Let's take it to the kids now. What do they do when presented with our conversion confusion?

The instructions in the problem were to round to the nearest tenth. The students' answer was 5 feet 8.6 inches. Is there a better answer?