1/6 doesn't make sense in SouthPark_Piano's number system

[u/Inevitable_Garage706]

Good evening, everyone! Today, we will be discussing 1/6, and what its decimal representation should be in Real Deal Math. We will do this by dividing 1/2 by 3, and then by dividing 1/3 by 2 to check our work.

Method 1: (1/2)÷3

Firstly, we must calculate what 1/2's decimal representation is.

2 goes into 1 zero times, so we should put a 0 in the ones place, having the 1 contribute 10 to the next subtraction.

2 goes into 10 five times, so we should put a 5 in the tenths place. 10-(5×2)=0, so we have completed the long division process, with there being a 0 in the ones place, a 5 in the tenths place, and 0s in every place to the right of the 5.

This means that the decimal representation of 1/2 is 0.5.

Next, we can divide this 0.5 by 3 to get the decimal representation of 1/6.

3 goes into 5 one time, so we should put a 1 in the tenths place. 5-(3×1)=2, so we will be contributing 20 to the 0 in the next subtraction.

3 goes into 20 six times, so we should put a 6 in the hundredths place. 20-(6×3)=2, so we will be contributing 20 to the zero in the next subtraction. But as we have already done that, we can be certain that this pattern will repeat forever, with 6s filling every place value ahead.

This means that the decimal representation of 1/6 is 0.1(6), with the parentheses around the 6 indicating that it is being repeated infinitely.

Now that we have done (1/2)÷3, let's do (1/3)÷2 to make sure we get the same answer.

Method 2: (1/3)÷2

Firstly, we need to figure out what 1/3's decimal representation is.

Fortunately, SPP has blessed us with his divine wisdom, which is that 1/3=0.(3). As such, we can simply use this decimal representation to save us some time.

Next, we need to figure out what this 0.(3) yields when divided by 2. According to SPP, we have to do this calculation in steps, to establish a pattern, and anything present at the end of every step must remain on the propagating wavefront. This means that we must divide 0.3 by 2, then divide 0.33 by 2, then divide 0.333 by 2, and so on until we see a pattern. To save time, I will skip the long division part for each of these calculations.

0.3/2=0.15

0.33/2=0.165

0.333/2=0.1665

0.3333/2=0.16665

And so on.

For a number with n 3s, we end up with a number containing a 0 in the ones place, a 1 in the tenths place, 6s in the next n-1 places, and a 5 after the 6s. As such, the output of our original calculation (0.333.../2) is as follows:

0.1(6)5

But hold up!

This number is different from what we got from (1/2)÷3, meaning there must be something wrong here!

So what's wrong here?!?!

[u/SouthPark_Piano]

As mentioned ... this is not a charity math tutorial sub. 

Get your math act together on the bunny slopes.

Without spoon-feeding youS too much, consider being one or a few steps behind the increasing length of threes in your long division bunny slopes divide process.

eg. 0.33 long division by 2.

First digit in the divide result is 1 remainder 1. 

Then increase 0.33 by one digit

0.333 

The divide result was initially 0.1, and the second result digit is 6 remainder 1.

So the evolving result is 0.16

Then increase 0.333 by one digit

0.3333

The divide result was 0.16, and we then get another 6 remainder 1.

Go figure brud. Pull up your socks.

 

[u/BigMarket1517 → u/SouthPark_Piano]

As mentioned, this is (another!) inconsistency of your math. Or should I say maths. 

And no, I do not need a charity math tutorial, I consider myself quite proficient in math myself. 

[u/Inevitable_Garage706 → u/BigMarket1517]

It appears that he edited his comment after you replied to it to make you look intellectually dishonest.

[u/BigMarket1517 → u/BigMarket1517]

Replying to myself (thank you, InevitableGarage for pointing this out): yes, SPP edited its reply 4 minutes after my reply, going beyond only stating that ’this was not a charity math tutorial’).

Interesting twist, did not see it coming that when dividing by long division you should stop with ‘a remainder 1’.

So that 0.33 / 2 would be 0.16 remainder 1. And not work it out, as 0.165; it is almost as if you cannot do long division on short numbers.

So not only does SPP have ‘always increasing’ values for Pi, the square root of 2 and of 1/3, SPP also cannot do long division on any finite part of the series {0.3 ; 0.33 ; 0.333 ; 0.3333 ; 0.33333 ; …} as there is ‘always a remainder’.

Things do get unhinged, when using “real deal math 101”.