Why can't 10 be divided by 3 perfectly?

[Rocketman]

If you have a 10 inch ruler and you cut it into 3 equal parts, what would each part equal? Whatever the answer is, that number would STOP. It has to stop, because it's a physical object which can be measured.

Now, take that answer and apply it to a calculator. If you divide 10 by 3, you get 3.333333333 for infinity. How is that possible? Why can something be divided perfectly in a physical way, but mathematically last for eternity?

If you have a 10 mile strip of road, you can split up that road into 3 separate roads. But on a calculator, these roads last forever.

 

[Kane52630]

I hear dividing by zero helps.

 

[Immortalfire]

Do your own homework.

 

[chaseter]

If you have a 10 inch ruler and you cut it into 3 equal parts, what would each part equal? Whatever the answer is, that number would STOP. It has to stop, because it's a physical object which can be measured.

Now, take that answer and apply it to a calculator. If you divide 10 by 3, you get 3.333333333 for infinity. How is that possible? Why can something be divided perfectly in a physical way, but mathematically last for eternity?

If you have a 10 mile strip of road, you can split up that road into 3 separate roads. But on a calculator, these roads last forever.

The correct answer is that you won't be able to perfectly divide a 10 inch ruler by 3. Put them under a microscope and they won't be equal. You would be off some minuscule percentage. That is what the calculator is trying to tell you. You try your hardest to make them all perfectly equal but you won't be able to.

 

[Gwendolyn Stacy]

Ask the guy who invented the calculator.

 

[TLH]

If you have a 10 inch ruler and you cut it into 3 equal parts, what would each part equal? Whatever the answer is, that number would STOP. It has to stop, because it's a physical object which can be measured.

Now, take that answer and apply it to a calculator. If you divide 10 by 3, you get 3.333333333 for infinity. How is that possible? Why can something be divided perfectly in a physical way, but mathematically last for eternity?

If you have a 10 mile strip of road, you can split up that road into 3 separate roads. But on a calculator, these roads last forever.

Simple: it's impossible to cut a 10-inch ruler in 3 equal parts. One part will be microscopically (undetectably) larger than the other two.

 

[Ultra Lantern]

Do your own homework.

I agree with Immortalfire.

 

[Enriquespy]

The parts will be equal, but the measure comes from an arbitrary source.

 

[Asteroid-Man]

I was going to suggest that you convert it to cm (25.4) then divide that, but then you get 8.46 (to infinite). Hell even by metric inches you get ****ed over at 83.3.

 

[Calvin]

Jesus christ, does nobody understand fractions? You could cut a ten inch ruler into three equal parts that are 10/3 in. each. You don't have to do it in decimals, that's arbitrary, and it certainly isn't "impossible."

I certainly have rulers that can designate a third of an inch. Measure ten of those at a time, cut, and call it a day.

 

[Asteroid-Man]

My GOD!!! He's a genius!!

 

[Calvin]

Also, whoever is saying that something with a repeating decimal would stretch forever doesn't understand math. 10.333333.... wouldn't reach as far as 10.4, so it certainly doesn't stretch to infinity.

 

[PWN3R]

Man, **** math.

 

[SpideyVille]

Two's company, but Three's a crowd.

 

[Oddzball]

Also, whoever is saying that something with a repeating decimal would stretch forever doesn't understand math. 10.333333.... wouldn't reach as far as 10.4, so it certainly doesn't stretch to infinity.

While we're at it why won't 1 + 1/2 + 1/4th taken to infinity be greater than two"?

 

[Calvin]

While we're at it why won't 1 + 1/2 + 1/4th taken to infinity be greater than two"?

Well, to put it in practical terms, if you think of the distance between one and two, and you can only walk half the distance remaining each time you walk, I think you'll be able to visualize why it won't be greater than two. Technically, you won't ever reach two, but as you approach an infinite number of attempts, the distance you have left to travel becomes so small that you are "approaching" two as you extend the number of attempts to infinity.

 

[Llama_Shepherd]

If you have a 10 inch ruler and you cut it into 3 equal parts, what would each part equal? Whatever the answer is, that number would STOP. It has to stop, because it's a physical object which can be measured.

Now, take that answer and apply it to a calculator. If you divide 10 by 3, you get 3.333333333 for infinity. How is that possible? Why can something be divided perfectly in a physical way, but mathematically last for eternity?

If you have a 10 mile strip of road, you can split up that road into 3 separate roads. But on a calculator, these roads last forever.

This question is based on a hypothesis. A hypothesis based on a profound misunderstanding of numerical value. 1 cannot be divided by 3 because you cannot get three equal parts. Using rational numbers you get 3 with a remainder of 1 or 3.3 with a remainder if 0.1. Without using remainders you get an irrational number (ie a number that can never have a physical representation, ie infinitely long). But just because a number is infinitely long, doesn't mean that is infinite in value, the number 4 has a greater value than 3.3 recurring. One third cannot be represented as a percentage, nor a decimal. It just means that if you had an infinite amount of time to write down the number, after that, you would find the true answer, but it would take you an infinite amount of time to do so, hence the irrationality of the number.

 

[Hound55]

Jesus christ, does nobody understand fractions? You could cut a ten inch ruler into three equal parts that are 10/3 in. each. You don't have to do it in decimals, that's arbitrary, and it certainly isn't "impossible."

I certainly have rulers that can designate a third of an inch. Measure ten of those at a time, cut, and call it a day.

Technically there are no rulers that can designate a third of an inch... But they get close enough that the human eye could never differentiate.

 

[chaseter]

Jesus christ, does nobody understand fractions? You could cut a ten inch ruler into three equal parts that are 10/3 in. each. You don't have to do it in decimals, that's arbitrary, and it certainly isn't "impossible."

I certainly have rulers that can designate a third of an inch. Measure ten of those at a time, cut, and call it a day.

There are no 1/3 of an inch marks on a ruler. You know why? Because 1/3 of an inch is 8.466666666-------7 mm.

Also, a fraction like 1/3 is simplified instead of writing 0.333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333.

It is not physically possible to have 3 equal parts of 10 because you can magnify the parts by 10,000x and see that they are not in fact equal because the number is infinite.

 

[Aesop Rocks]

I can count to potato.

 

[Hound55]

I can count to 'more' in potatoes...

 

[Calvin]

Technically there are no rulers that can designate a third of an inch... But they get close enough that the human eye could never differentiate.

I'm pretty sure that's incorrect, other than human error, there's nothing mathematically limiting a ruler from designating a third of an inch, especially it you let a computer and or/robot correctly calibrate it. Hell, you could have a graphing program perfectly designate third of an inch markers and just print it out, and the accuracy would only be limited by how exact the printer is. There's certainly nothing mathematically keeping you from designating thirds of a unit of measurement, which you seem to be implying. If your point is just that humans can't or won't do things mechanically perfect, then that's really just a meaningless and useless point, especially for a mental exercise.

 

[Calvin]

There are no 1/3 of an inch marks on a ruler. You know why? Because 1/3 of an inch is 8.466666666-------7 mm.

I have definitely used rulers in the past with inches split into thirds. My dad had a huge set of triangular rulers with different designations in different units on each face of the ruler, and I very clearly remember one of the rulers having a side with inches split into thirds.

 

[Calvin]

There are no 1/3 of an inch marks on a ruler. You know why? Because 1/3 of an inch is 8.466666666-------7 mm.

Also, a fraction like 1/3 is simplified instead of writing 0.333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333.

It is not physically possible to have 3 equal parts of 10 because you can magnify the parts by 10,000x and see that they are not in fact equal because the number is infinite.

I think you're mixing this up in your head. 1/3 is not an approximation of .333333 to infinity, it's the actual representation of that in fractal form. The actual length of an inch is an arbitrary human choice. If you were the person to decide what an inch was, you could take a single stick, and say "an inch will be this length times three" and then a third of an inch would be the exact length of the stick. There is nothing mathematically limiting here about using fractions, and technically no need to approximate.

 

[chaseter]

I have definitely used rulers in the past with inches split into thirds. My dad had a huge set of triangular rulers with different designations in different units on each face of the ruler, and I very clearly remember one of the rulers having a side with inches split into thirds.

I think Hound said it best that the human eye cannot differentiate between such a small percentage of error that it doesn't matter. But, if you put each piece under a microscope you would see that they are in fact, not 3 equal parts.

Example, what is 1/3 of an inch? It's not a definite number. It is infinite so technically speaking, there is no true 1/3 of an inch or 3 equal parts of 10. As I said, 10/3 is 3 1/3 and 1/3 is an infinite number simplified into a fraction.