Hello.

When you divide 10 to 3 (10/3), you will receive an answer of 3.3 (where 3 is infinite) \(3.\bar{3}\)

Since, it is repeating decimal, it will continuous to expands the 3.

However, if I ever wants something to be exacted. What should I do with this infinite 3? How many 3 should I put? Or should I round off the 3? Or what?

Thanks

 

That is always a core problem with math. In the real world, you don't need that many decimal places though. Once you measure dimensions smaller than atoms it all becomes moot. I'm not sure off the top of my head where this occurs, but I think it is in the realm of 12 to 20 decimal points.

Past that you enter the world of chaos theory, where extremely small changes cause big changes somewhere else.

 

The answer is it depends on your needs. If I'm doing some rough carpentry work, I usually round the dimensions to the nearest tenth of an inch (my tape measure is graduated in decimal inches). Even better, since my tape measure also is graduated in mm, I virtually always just measure to the nearest mm (the mm is my favorite practical length unit because most carpentry and home projects just need to be measured to around the nearest mm).

If I'm doing machine work like making a close slip fit of a shaft to an existing hole, I'll measure e.g. to the nearest 0.0001" and turn the shaft to within a few 0.0001" of the desired size.

As you gain experience, you virtually always can decide how many significant figures you need in an answer. I've been a scientist for many decades and it's quite rare that you need more than 5 or 6 significant figures for any practical work. Some exceptions might be when working in a metrology lab or performing exacting measurements of a subtle physical phenomenon (for an interesting example, go look at the work Michelson did about a century ago on measuring the speed of light, as his calculations are available on the web).

 

That is always a core problem with math. In the real world, you don't need that many decimal places though. Once you measure dimensions smaller than atoms it all becomes moot. I'm not sure off the top of my head where this occurs, but I think it is in the realm of 12 to 20 decimal points.

Past that you enter the world of chaos theory, where extremely small changes cause big changes somewhere else.

Exactly.

I remember somebody said, here in forum, that if you are about to atoms. You are going to use 3.333333333 I don't know if how many 3s.

But is there any standard???

 

Like Someones Dad stated, it depends entirely on your application. When I am making home brew parts I use 2 decimal places. Most machine shops use 3, a very few go to 4 or 5 decimal places. Carpenters use 1 or 2 decimal places.

 

If you are concerned about solving math equations though, your best bet is to leave it at its fraction form 10/3. Don't underestimate the power of fractions, they're often more useful than decimals.

 

I can't argue that point, but I love my scales (specialized rulers that are marked down to 0.01").

For most electronic applications I prefer decimal places. Any machine measurements generally use decimal places. Humans tend to think in fractions though, which explains carpenters.

 

I was taught that three "periods" indicates a repeating decimal. That means that 10/3 = 3.333...

enough numbers to define what is repeating then three dots.