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Hi, I am confused. When a # is halfway to the next multiple, my book says to round up or down. So 35 can be rounded to 40 or 30 and 65 can be rounded to 70 or 60, and 445 can be rounded to 440 or 450? How do I know to round up or down in these situations? Thanks!
The most common method is to round up. So 35 rounded to the nearest 10 would be 40.
If the last digit is a 5, round up. This is so that there is an equal number of digits that round down (0, 1, 2, 3, 4) as there are that round up (5, 6, 7, 8, 9).
ok, so -14,525 rounded to nearest 10 is -14,530? my book's answer is -14,520. Is there a right or wrong answer?
-14 520 is greater than -14 530, so the book has correctly rounded up.
I see, because its a negative # and the -14,520 is more positive than -14,530. Correct?
Yes
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In numerical work, it is usual to round exclusively to either an even or odd digit. That way you round up roughly half the time and down roughly half of the time.
Take for example the addition of the sequence of numbers 12.5, 33.5, 17.5, 21.5, 42.5, 8.5 .
Retaining the .5's gets you an 'actual' total of 136, while rounding up in each case gets you 139.
If you choose to round to an even digit in each case you get the sequence 12, 34, 18, 22, 42, 8 with a total of 136, equal to the 'raw' total.
I suppose an advantage of always rounding up is that you know that your total will always be greater than the 'actual' total whereas rounding to an even or an odd digit you could be greater or less than the 'actual'. You will pretty much always be closer though.