In MGMAT Equations, Inequalities
, and VICs, Chapter 12 Question 5, you are given the length of a bicycle path as 225 miles long, rounded to the nearest mile. I chose the wrong answer on this question because I believed that 225 miles rounded to the nearest mile would make the path a length of anywhere from 224.5 miles to 225.4 miles. The official answer says that the cyclist must have ridden between 224.5 and 225.5 miles to fulfill the rounding requirement. This makes no sense to me. 225.5 rounded to the nearest mile is 226. What am I missing here???
You are correct theoretically. But, while solving questions like these where you have to calculate average, you should round it off to its closest approximation and a convenient decimal.
Ideally; 224.50000000000000000000000<=x<=225.499999999999999999999999999999999999999999 should be rounded to 225 and 225.500000 should be rounded to 226.
But, when you need to use these rounding to calculate your speed, it is best if you used a more workable number like 225.5 rather than 224.99999999999999999999999; 225.5 and 224.9999999999 are almost the same. Also, 224.99999999 is closer to 225.5 than it is to 225.4000000 and will incur more appropriate result.
P.S.: For the questions(PS/DS) specific about finding the hundredths place digit and thousandth place digit, you would use the theoretical concept as you have mentioned.