If dividing by zero gives a "Math error" why doesn't divide by 3?

Question

When you attempt to divide by zero on a calculator it gives a "Math error" notice or similar. If you try to divide 1 by 3 however, it does not. You can't divide 1 by 3, though.


Because 0.333333333 times 3, is 0.999999999, and not 1. Why is this?

Answer 1

A calculator can be constructed to report "infinity" as an answer; however, infinity is not a real number in the sense that mathematicians define real numbers. That is one reason why calculators do not accept division by zero, but there is an even more compelling reason: if division were allowed, it would be possible to "prove" that any number equaled any other number and all sorts of absurd results, effectively destroying the value of mathematical proof altogether. You may even have run into an example of such a "proof" that 1 = 2 in which the argument disguised the necessary step of division by zero to fool the unwary.



Many calculators store fractions internally as decimal or binary equivalents to a finite precision - they cannot store such a number to an infinite number of decimal places. On such a calculator, a division resulting in a nonterminating fractional part will therefore be in error by a small amount. When this approximation is then multiplied again by the original divisor, the result will be close to but not quite the same as the original dividend.



Some calculators are able to store most rational numbers exactly, provided that the magnitude of the two integers comprising the ratio is small enough not to overflow the capability of the calculator's memory. The calculator that comes with the Windows operating system is of this type. However, even these calculators are subject to roundoff errors when asked to handle irrational numbers like √2 or π.

Answer 2

The by zero is just a rule. It is undefined because how can you divide something by nothing. I mean do any division. Lets say 2/0. If you do it by hand then 2/0 = 0 remainder 2. Then you divide 20/0 and the answer is 0.0 remainder of 2 so on and so forth. It will never end. The computer would run out of memory. Is not the same as 0/2 because you know that 2*0 = 0 and that will satisfy what you are looking for. 2/0 there is no answer that will satisfy it.



The thing with decimals is that they are not accurate. 1/3 is more accurate than 0.3333333. As a matter of fact take 0.333. This number is less accurate than 0.3333 or 0.33333. The more numbers you have the more accurate it is. Machines have a degree of accuracy and there are rules governing how to round off numbers. It all depends on the mathematical operation you are doing. In machines there is a floating point unit that can give decimals to a certain degree of accuracy. It also all depends on what you define things as. For most things 0.999999 is 1. However, there are cases where you don't want to round up because it introduces inaccuracies. So, when you say 0.333333 you are giving an approximation. When you say x/0 you are saying divide a number by something that is undefined because there is really no number that exist that can give you an answer that wil be acceptable.



If you take calculus there is also a concept called limits. It kind of means that if you look at a number to infinity what does that number or that something behave like. For example lets take the 0.9999999999999999999. Instead of looking at it from the beggining 0.999 travel to the right way way far. Like a light year of travel to the right. What happens to that number. Well, it approaches 1. it never quite gets there but is so close. Is easier to visualize it with a graph. That number is so close to 1 that it might as well be one. That is for all intent and purposes it might as well be 1. It all depends on how picky you want to be. Things to 4 decimal places is pretty dam accurate for most things. Is al about how much does it matter to what you are doing. If you divide a pie into 3 pieces it really doesn't matter who gets 1mm more or less than the other person most of the time.

Answer 3

Hi:



the reason for this is due the way the calculator Does math;



to see why try to divide 1 by 3





3/1.000000000





3 can't divide into 1 So we put a 0 there and go to the next digit over the decimal So put in a decimal point and 10 divide by 3 is 3 ( 3*3= 9) So:





***0.3

3/1.00000000

*-0

--------

**10

***-9

---------

***1



and if you continue on with the division this make it :

.3333333333333333333...on to infinity with one trailing ahead of it



the Calculator can't hold a infinite number like that in it memory. Most



calculator hold about 8 to 9 digits on some scientific calculator's it twelve digits

now when try times that number by 3 you get .9999999999999 that because the calculator think your trying to multiply all the three's by 3

So what you get is .999999999...on to infinity. It can't round or know that it is one but you know that because your brain know that the one is in infinity Hope this answers question # 2



For question #1:



You have to think about this one :



Start by asking yourself: what is division?



Your answer should be: repeated subtraction (until you reach zero or lower) or it's multiplication in reverse



To see what I'm talking about let do a division ( I know you know how to do this. But humor me. Okay?)



6 divide by 3



repeated subtraction method:



6 - 3= 3(1) 3-3 = 0 (2) { the () is to keep track of the # of time the subtraction is used}



we had to subtract 3 from 6, two times to reach zero So this proves



2 * 3 = 6



the Multiplication method is



3+3 =6 since there are two 3 add together to get six So 2 *3 = 6



However when we try to divide by zero a stange thing happens



Let do one say 5/ 0 = ?



Subtraction method:



5- 0= 5 (1), 5-0= 5 (2), 5-0= 5 (3), .....etc

( doesn't reach zero or below) does it





0+0+0+0+0= 0 doesn't reach or equal 5; in fact you could any number of zeros to equal any other number of times and it will alway equal zero



this type of equation is undefine or infinte number of solutions



if the programmer and the makers of both calculater and computer don't put a catch a division by zero program flag to print division by zero Error or something like it. The thing would go to never never land { Meaning it would run without returning a display forever; unless you force it to stop} in try to solve this. Because of the above reasons .

Answer 4

Dividing by 0 is undefined. It is something that should NEVER be done!

As to 0.3333333333333333333... x3=0.9999999999... firstly the calculator rounds things (for example 2/3=0.6666666666666666... but the calculator makes it 0.666666667)

But it can be proved that 0.9999999999...=1 like so:

Let a=0.999999999... (the ... means it goes on infinitely)

then

10a=9.999999999...

taking the first away from the second:

9a=9

a=1

Therefore 0.999999999...=1

This works because 0.999999... is a recurring decimal. It goes on forever. This is done in the way that you work out what fraction is the equivalent to a recurring decimal.

Answer 5

1/3 is .333333(repeating) A calculator will simply round this.



The reason you get a math error for dividing my zero, is that you can't divide by zero. Example: You have two apples, and you want to divide them 0 times... You simply can't do that..

Answer 6

Dividing by zero is an undefined mathematical operation. Dividing by 3 is defined - you get a rational number. Like someone else said, your calculator is rounding off the 0.999999999999.



But in theoretical math, 0.99999 (with nines continuing to infinity) is equal to 1.

Answer 7

Dividing by 0 is undefined.



If I have a pie and want to divide it into 3 pieces, everyone gets 1/3 or 0.333.



Now if I ask you to take that same pie and divide it by nothing or 0, it makes no sense, hence, undefined.

Answer 8

because you cannot divide by zero, take a pie and try to divide it by zero, you can't. take a pie and divide it by three, you can. You see in the case of 0 it is not possible to divide by zero, therefore it is an error. dividing by 3 is possible. just might not get a smooth as number.

Answer 9

Cut a pie in 3, then cut it in 0. 'Ti Tuga digga tu Gi Friba fligugibu Uh Fligugigbu Uh Di Ei Friba Du Gi Fligu fligugigugi Flilibili Ah Bow Bow Bow Ooh Bow Bi Fligu wene mamamana Sacrebleu

Answer 10

-- division by zero = infinity (or approaches it) and calculators have a little trouble displaying infinity



-- 1/3 does equal 0.33333... and 0.9999.... does equal 1

let x = 0.333... repeating

then 10x = 3.3333...

10x - x = 3.3333... - 0.333333...

9x = 3

x = 3/9

x = 1/3

Answer 11

Because your calculator is rounding off.

Answer 12

That's just the way it is.