What would be the proper rounding to the answer of this math problem

The sum of the length and the width of a proposed feed lot is 1500 ft. Find the length and width if their ratio must be 5:2.
5x + 2x = 1500
x = 214.2857143

Assuming 1500 ft is a measured value with two significant figures, but the 5:2 ratio is exact, you can use the multiplication and division rule when finding 2x or 5x, so

2x = 2(1500 ft / 7) = 429 ft

which is 430 ft to two significant figures.

Then use the addition and subtraction rule for finding the other dimension, keeping one insignificant digit to prevent accumulated rounding error

5x = 1500 ft - 429 ft = 1071 ft

which must be rounded to the hundreds place, or 1100 feet, so the answer would be

430 ft and 1100 ft.

If you find 5x first, then

5x = 5(1500 ft / 7) = 1071 ft

which is 1100 ft to two significant figures.

Then use the addition and subtraction rule for finding the other dimension, keeping one insignificant digit to prevent accumulated rounding error

2x = 1500 ft - 1070 ft = 430 ft

which must be rounded to the hundreds place, or 400 feet, so the answer would be

400 ft and 1100 ft

I was hoping the two calculations would turn out the same, but no such luck. I'd go with the first approach, as 430 ft has more significant figures than 400 ft.

You're welcome. I'm glad to help.

Report Abuse