(0 we just truncate, since it doesn't affect the previous digit at all.) OK, let's see if I can explain this. However, the point is to be able to square these numbers in your head without using a calculator, and once you get into triple-digit numbers above 115, it's a little hard to use this procedure in your head. The problem lies in that a '5' should be rounded up or down depending on if it's preceding digit is odd or even, and this behaviour should be observed all the way through all decimals from right to left..?
Here are some more examples for rule #3. The first two rules are more-or-less the old ones. Notice the different phrasings of the problems. Would your teacher be so mean as to include problems like this one on a test?
I saw its allways rounding down on Odd numbers. The typical rule taught is that you round up with five or more and round down with four or less. Suppose you had a very large sample of numbers to round off. Try this solution - You might need to scale your number to the right size so the Modulo will work correctly. Thus we're rounding up more than rounding down, and we have a positive systematic error.
This last one is tricky (at least for high schoolers being exposed to this stuff for the first time!). The following rules dictate the manner in which numbers are to be rounded to the number of figures indicated. The @s in my querry was used to deterine on which digit it should round. Notice that 5, if rounded up always, gives us 5 numbers we round up, and 4 we round down.
0.245 = .24 round down. However, please do not rush off to your elementary school teacher and read 'em the riot act!
The answer is 23.6. rounding "off" (keeping the number the same) in fifty percent of the roundings-even numbers followed by a 5. The nine rounds off to a ten (not a zero), so the correct answer is 2.050, NOT 2.05.
Example #1 - Suppose you wish to round 62.53Now that "everyone" has a calculator that will give a result to six or eight (or more) figures, it is important that we know how to round the answer off correctly. Here are some more examples of the "five rule." So multiply by the power of 10 of the rounding digits in the 2nd part... Hope this helps For example, in 2.0495, let's say we want to round off to the nearest 0.01. Whenever the decimal value you intend to round off is 5, you must look at the previous values, before decimals ALSO. To do this, you must look at the hundreths place (remember, we are going to keep the tenths place in our answer). YOur Number and which digit to round. To do this, you must look at the hundreths place (remember, we are going to keep the tenths place in our answer). However, the important number in this problem is the nine, so the rule is to round up and the correct answer is 2.05. Round off at the five.
When the first digit dropped is 5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e., round off to the nearest even digit).
This means the average of the values AFTER rounding off would be greater than the average of the values BEFORE rounding. In both cases, you have to look at the digit just to the right of where you intend to wind up in your answer.
If it is odd, you round up. Then, on average, the roundings "off" will cancel out the roundings "up."
Example #5 - Round 23.55 to the 0.1 place.
Since we are rounding off a 5 (in the hundreths place), we must round to an even number. This Version scales the numbers so i can compare if its an odd or even digit right before the rounding place.
If you are to round off the the 0.01 place, you have to look at the 0.001 place as well. In the ChemTeam classroom, the sufferers (oops, I mean students) have learned to shout "YES" in unison to such easy questions. The digit you are examining is the first digit to be dropped. Rule three is the change in the old way.
It is a five, so now we look at the next digit inward (the tenth place) and see it is a five, an odd number. For example, numbers like 3.65 or 3.75, where you are to round off to the nearest tenth. One says to round off to a specific number of significant figures and the other type says to round off to a specific decimal position.
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