# What is the common way to round up this number?

1. Feb 22, 2013

### cdux

0.444448

I want 4 digits.

Is it 0.4444

or is it

0.4445 because I say "since the next one becomes 5 because of the 8 then I consider the previous one a 5 as well"?

2. Feb 22, 2013

### DrewD

Re: Re: What is the common way to round up this number?

It is less than halfway between 0.4444 and 0.4445 so you should not round up.

3. Feb 22, 2013

### cdux

So, should it be limited to 0.44445 (from 0.444448) even if one aims for 4 digits?

edit: Also I'm not sure what 'less that halfway' means (in this context).

4. Feb 22, 2013

### Simon Bridge

The rule is to round to the value that the number is closest to.
0.4444 <---<<< round down value
0.444448 <---<<< the number being considered
0.44445 <---<<< half-way mark (thanks DrewD)
0.4445 <---<<< round up value

0.444448 is closer to 0.4444 than it is to 0.4445 so you round down.
This is why the rule-of-thumb is that you only need to consider the next digit along when rounding.

5. Feb 22, 2013

### ModusPwnd

This is also the reason you don't want to round "along the way" in your calculations. You try to do all of your rounding at the end, otherwise multiple roundings can compound and give you the wrong answer like they did here.

6. Feb 23, 2013

### Staff: Mentor

Which means either (a) you keep your numbers in your calculator (using memory registers if necessary) throughout the calculation until the end, or (b) you do all the algebra first, symbolically, to get a single formula for your final result, then plug your numbers in and calculate the result all at one go in your calculator.

7. Feb 23, 2013

### cdux

Ah thanks, I get it now. I should be thinking "it's 0.4444 because the 48 that follows is still lower than 50".