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7075.471698 technically rounds to 7075. Less than 0.5, round down. 0.5 or greater, round up.[1] But saying "what's the least" and then "round your answer" at

7075.471698 technically rounds to 7075. Less than 0.5, round down. 0.5 or greater, round up.[1] But saying "what's the least" and then "round your answer" at the same time is silly. If you ask a student "each bus holds 10 people; how many buses do you need to move 32 people?" the answer is 4. I would hate to be asked to "round" that answer. 7075 rupees is too few; 7076 is the first whole number that is "enough." The real meat of that question comes down to the student being able to figure out "do you multiply by 0.96, or do you divide by 1.04?" And the sample exchange with the fee is pure filler to distract the student. EDIT Rerad Blackjack31's link, and you will find the original question, which isn't as butchered as it seems at The Atlantic. The present the example rate because they first ask the student to calculate the exchange rate. END EDIT Plus, what about fluctuations in the daily exchange rate? The student is supposed to assume that isn't changing, but then why in the world are we talking about the daily exchange rate? Say it's a fixed exchange rate. [1] I had a third grade teacher who insisted you could round to the tenths position and then the unit position, and always get the same answer if you just immediately rounded to the unit position. This is the test case that proves her wrong, but for some reason she didn't want to hear it.[2] [2] I was in some ways a prat.

Chinjut 12y ago
I'm glad you pointed this out to your teacher. It is worth noting, though, that if it weren't for the arbitrary "If it's exactly halfway inbetween, you should just round it up" rule taught as received wisdom in school, your teacher would've been on stronger ground. And it is reasonable that they were attempting, in their way, to convey (or even fully come to terms with themself) the understanding that the nearest integers to a value are always also among the nearest integers to the nearest multiples of 0.1 to that value (and all the generalizations of this); it's just that sometimes there are other nearest integers to nearest multiples of 0.1 as well.
- danielweber 12y ago
  The "0.5 rounds up" is kind of arbitrary, but it has the advantage of "you only need to look one digit out to round." 4.49 obviously rounds to 4. 4.51 obviously rounds to 5. 4.50, since it "should"[1] follow the same rules as any other number that starts with "4.5", thus rounds to 5. Say I were looking at a real number of arbitrary length, such that it starts with 4.500000000000... and maybe has a non-zero digit somewhere in it before it terminates. With the "round up on .5" rule, I don't have to keep on reading out indefinitely to round it. [1] This "should" is assertion.

Chinjut 12y ago

I'm glad you pointed this out to your teacher. It is worth noting, though, that if it weren't for the arbitrary "If it's exactly halfway inbetween, you should just round it up" rule taught as received wisdom in school, your teacher would've been on stronger ground. And it is reasonable that they were attempting, in their way, to convey (or even fully come to terms with themself) the understanding that the nearest integers to a value are always also among the nearest integers to the nearest multiples of 0.1 to that value (and all the generalizations of this); it's just that sometimes there are other nearest integers to nearest multiples of 0.1 as well.

danielweber 12y ago
The "0.5 rounds up" is kind of arbitrary, but it has the advantage of "you only need to look one digit out to round." 4.49 obviously rounds to 4. 4.51 obviously rounds to 5. 4.50, since it "should"[1] follow the same rules as any other number that starts with "4.5", thus rounds to 5. Say I were looking at a real number of arbitrary length, such that it starts with 4.500000000000... and maybe has a non-zero digit somewhere in it before it terminates. With the "round up on .5" rule, I don't have to keep on reading out indefinitely to round it. [1] This "should" is assertion.