"Rounded to the nearest" - What does that term mea

Nearest mile, as I understand, is 0.5 < X < 1.5 because
anything slightly above .5 is nearer to 1 than to 0 and
anything infinitesimally less than 1.5 is nearer to 1.
For example anything between 224.50000....1 to 225.499......9
should be 225. You can approximate this range to be between
224.5 and 225.5 and make your calculations.

0.5, I think, is counted nearer to the next digit.

HTH

rrobiinn wrote:I found this term in the following math.

A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest
mile. If the trip took him 5 hours, rounded to the nearest hour, then his average speed
must be between:
(A) 38 and 50 miles per hour
(C) 40 and 51 miles per hour
(E) 41 and 51 miles per hour
(B) 40 and 50 miles per hour
(D) 41 and 50 miles per hour


Please explain how to round to the nearest with examples.

Hi!

"Rounding" means evening things off to the nearest unit mentioned.

For example, "rounded to the nearest mile" means that you eliminate all decimal points. "Rounded to the nearest hour means that you ignore minutes and seconds.

To properly round off, you can round either up or down depending on exactly how far away you are. If you decimal is .5 or greater, you round up; if the decimal is .4 or lower, you round down.

For example, 35.6 miles "rounded to the nearest mile" would be 36 miles. 35.4 miles "rounded to the nearest mile" would be 35 miles.

Similarly, 5.7 hours would be rounded up to 6 hours; 5.4 hours would be rounded down to 5 hours.

Applying that info to this question, we know that the path is 225 miles, rounded to the nearest mile - so the actual length could be between 224.5 miles and 225.4 miles; the trip took 5 hours, rounded to the nearest hour, so the actual time could be between 4.5 hours and 5.4 hours.

To solve, we need to find the range possible rates. To maximize the rate, take the biggest possible distance and the smallest possible time; to minimize the rate, take the smallest possible distance and the largest possible time.

Max: 225.4 miles, 4.5 hours
r = 225.4/4.5 which is almost exactly the same as 225/4.5 = 50

Min: 224.5 miles, 5.4 hours
r = 224.5/5.4 which is almost exactly the same as 225/5.4 = 41. something

So, we need a range that encompasses both 41 and 50... choose C!

(I'm assuming that the letters are correct, even though the answers are given out of order.)

* * *

As an aside, if you were to approach this by strategic elimination you could narrow down the answers to A and C, since the range in C encompasses the ranges in E, B and D - so if one of those were the correct answer, C would also be correct! Since there can only be one right answer, E, B and D are all out of the running.

rrobiinn wrote:I found this term in the following math.

A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest
mile. If the trip took him 5 hours, rounded to the nearest hour, then his average speed
must be between:
(A) 38 and 50 miles per hour
(C) 40 and 51 miles per hour
(E) 41 and 51 miles per hour
(B) 40 and 50 miles per hour
(D) 41 and 50 miles per hour


Please explain how to round to the nearest with examples.