When I ask a calculator to divide 100 by 3, it says 3.33333recuring, but when I ask a calculator to multiply 3.33333 by 3, the answer is 9.999999recuring. How do mathematicians make complex mathematical equations if they cant even divide 100 by three?
someone please explain.
15 Answers

100 is not divisible by 3 when u divide 100 by 3 u get 33.333333…… not 3.33333…..
the good explanation of your answer is that 0.999999….is equal to 1
we can prove it by the following way:
let x=0.9999….
then 10x = 9.999999…..
subtract we will get 10x – x = 9.9999…. 0.99999……
which gives us 9x = 9 and therefore x =1
i hope this will help u with your confusion

That is what happens with repeating decimals — you get rounding errors.
In this case, it can be avoided by leaving the division in fraction form, ie:
100/3 = 33 1/3 This is precise. If you multiply THAT back again, by 3:
100/3 X 3 = 100, exactly, no error.
The problem arises in converting from a ratio of two integers, which is a RATIONAL number, to a repeating decimal which is not.

This is because 3 recurring means there are an infinite amount of 3’s after 33. This means that your answer will always have a string of 9’s behind it. The best you can do is leave it in fraction form as 100/3 if you want to be completely accurate.

because we don’t need a calculator to divide 100 by 3, so when we multiple it by 3, we get back 100.

100 Isn’t divisible by 3. That is just a fact. There are many mathmeticians that have more than proven this over the last 2008 years. Get a grip on reality dude.

100 divide by 3 is 3.333333
or you can put down the answer is: 3 R1 (remainer1)

100 divided by 3 = 33.333333333333333333 recurring
3 times 33.333333333333333333 recurring = 100
Reread your question – you have used three point three recurring, when it SHOULD be thirtythree point three recurring. The real calculations are fine… mathematicians are fine….
You have just made an error in your OWN calculations.
Go ahead – try it again with your own calculator.
Source(s): My calculator 🙂 and common knowledge of math. 
There are two aspects. First, calculators are not particularly good at representing nonterminating numbers, and that carries over into multiplication of them. Most physics/chemistry/etc done on computers is not hurt by this imprecision, as there is nearly always a larger source of error involved.
More interestingly, 99.9999recurring = 100, precisely (by series proof).

OK. Many have this same problem. The most precise that you can get is : 100/3. However 3.33333 repeating is the most “fractionless” way to say 100/3. I hope this is the BEST way to ANSWER your question!

To fuel a debate that keeps on going despite the clear math behind it, 0.9999… repeating is exactly 1. Exactly 1. Not almost one, not rounded off to one. It’s identical to one.
Google for a fuller explanation if you wish, but if you don’t agree, invent a system of mathematics in which it isn’t true. In the system of math we have, that’s the way it works.