How come it's usually stated earth's axial tilt is 23.5 degrees?

[mzatanoskas]

When it should be either 23 or 23.4, or 23.44 or some other appropriately rounded amount?

 

[swansont]

That's the value if it's rounded to the nearest half-degree

[mooeypoo]

For the same reason that "g" of gravity is usually states as 9.8m/s^2 when it's closer to 9.78 in sea-level, and a year is defined as 365 days when it's actually more like 365.25 days.

 

When you don't do complex or accurate mathematical calculations on these values, there's not much need to over complicate things by remembering the exact number. Kids, for instance, will treat gravity as if it's 10m/s^2 which is even further away from its accurate value; it's all about finding a compromise between having it easy to remember and calculate and accuracy.

 

We round numbers so it's easier to handle them in day-to-day basis. We look up and use the actual value when we do mathematical calculations.

[doG]

When it should be either 23 or 23.4, or 23.44 or some other appropriately rounded amount?

 

Back at 'ya... What is an appropriately rounded amount for 23.44? Would 23 or 23.5 be the better answer?

[mzatanoskas]

I get the general logic for rounding numbers, I just remember being told by my Maths teacher once a long time ago that numbers were always rounded in a set way in science, according to how many digits you used; 0.5 and above would be rounded to 1 (accurate to 0 decimal places) and 0.4 would be rounded to 0. (or something like that, I don't really remember which was why I was asking)

 

So 3.14159265 could be expressed as 3.14 or 3.142 and 23.44 could be expressed as 23, 23.4 or 23.44 etc accurate to the relevant number of decimal places.

 

However if you can also round up to the nearest "half" a decimal place, different people could over time round a number to a completely inaccurate result.

 

Ie 3.33 rounded to the nearest "half" a second decimal point is 3.35, round that accurate to one decimal place you get 3.4, round to a half, 3.5, then to 4, then to 5 then to 10.

 

Thinking about it again, I guess it's probably more a linguistic thing where people prefer to talk about "twenty three and a half" rather than saying "twenty three point four." I just thought the scientists would have been more pedantic. I know I would have lost marks for that at school!

[mooeypoo]

Well, there's no real accepted way of rounding all numbers in science, it all depends how accurate you want your result to be.

I guess the most common method is to use 2 decimal digits, but when you deal with really small stuff (like nm, ps, etc) that usually are presented by multiplication of 10 to the negative number, then you need much higher accuracy in the decimals.

 

You need to understand that rounding results will result in margin of error. In order to decrease that error you should avoid rounding. But that's not always possible.

 

For instance, take pi. Pi has infinite decimal numbers, so at some point you will have to round it in order to use it. Your decision where to round it (are you going to use 2 decimals? 3? maybe 10?) is up to you, as long as you are consistent.

 

That is, if you chose to use 5 decimal numbers, you should make sure that your entire calculation always uses 5 decimal numbers, and is consistent.

 

~moo

[Ophiolite]

I think you have to consider where you have seen the number 'usually rounded to 23.5 degrees'. I suggest that in most cases it was not written by a scientist, and perhaps not even by a science writer. Anywhere a scientist is using the number as the basis of calculations, or as an accurate record, then I think you will find it is presented accurately.

 

Even some (most) popular accounts will provide reasonable accuracy. Wikipedia, for example, gives 23.439281°.

It is also worth remembering that the angle varies over time.