# XI. Rounding Numbers

Rounding numbers has always kind of frustrated me. The number 3.5 rounded to the nearest integer. Would it be 3 or 4? If you came up with an answer, you have about a 50% chance of being wrong. Actually, if you said 4 you might have a 40% chance of being wrong. Let me elucidate (heh, heh - I just used elucidate in a sentence)!

We need to know how to do this, because in some situations we have to. If the bill comes to $3.786 after you multiply by the state tax percentage, we just change it to $3.79 because we can't give a fraction of a penny. We say that pi is about 3.14 because it is irrational and cannot be written down in it's entirety.

Where's the cut off? To the nearest unit or integer, to the nearest tenth, the nearest hundredth? The problem comes up when what we're exactly half-way in between two numbers. In other words, we are trying to figure out which number is closest to something .5, the fact is - neither number is closest.

## Rounding Numbers Half Up

Half Up - means that when there's just as much change whether you go up or down, you go up. So, 3.5 would become 4 and -3.5 would become -3. This seems to be a popular method when you're paying for something.

## Half Down

Hopefully you figured this one out. 3.5 would go to 3 and -3.5 would change to -4. Keep in mind this is only on exact halves. 3.51 would still round to 4, .51 is greater than half so you still go up. If it was less than half you would go down.

## Half Towards Zero

Here you go to whatever is closest to zero. So, 3.5 would drop to 3 and -3.5 would go up to -3.

## Half Away From Zero

Exhausting isn't it? You go to whatever is furthest from zero. 3.5 is 4 and -3.5 is -4.

## Half to Even

If you get an older book, this used to be the standard way. 3.5 would be 4 because 4 is an even number. -3.5 would be -4 because -4 is even. 4.5 would go down to 4 because 4 is even.

## Half to Odd

I think they just threw this one in there. I have never seen this used. Anyway, it would always go the half to the closest odd number 3.5 would be 3 and -3.5 would be -3.

## Stochastic

This method picks at random either up or down with a 50% chance of going either way.

## Alternating Tie-Breaking

This method keeps track of previous directions and if the last half went up, this one will go down. You would usually start this method with going up for the first occurrence and down for next one.

## Other Math Information

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__X. PEMDAS Order of Operations__

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