/sci/ - Science & Math

>>11478293
1÷3 > 0.3
1÷3 > 0.33
1÷3 > 0.333
1÷3 > 0.3333
1÷3 > 0.33333
1÷3 > 0.333333
... ad infinitum

1÷3 > 0.333...

>>10011621
lets take 1/3
1/3 × 3 = 1
What does 1/3 equal when converted from fractional to decimal?
It doesn't.
It always has a remainder, which lends to the fact there are always more 3's.
1/3 > 0.3
1/3 > 0.33
1/3 > 0.333
1/3 > 0.3333
1/3 > 0.33333
1/3 > 0.333333
1/3 > 0.3333333
...
1/3 > 0.333...

1÷3 does not strictly equate 0.333... in the same way 1÷4 strictly equates 0.25 or 1÷2 strictly equates 0.5
There is no strict equality of 1/3 in decimal notation. 1/3 is strictly greater than 0.333...

this lends proof to the following
[math]\frac{1}{3} > 0.\bar{3} \\ \big[ \frac{1}{3} × 3 \big] > \big[ 0.\bar{3} × 3 \big] \\ \frac{3}{3} > 0.\bar{9}[/math]

>>10007546
Stop posting this bait image and learn to do math

Green doesn't know how multiplication works
> 0.99 × 10 = 9.90
> 0.[infinite 9's] × 10 = 9.[infinite-1 9's, and 0], not 9.[infinite 9's] for a total of infinite+1 9's
Brown doesn't know how division works
>1÷3 always has a remainder, thus it's result in decimal is less than the fraction 1/3, rather than having a true equality in decimal
>[math]\frac{1}{3} > 0.\bar{3}[/math]
>[math]\big[ \frac{1}{3} × 3 \big] > \big[ 0.\bar{3} × 3 \big] [/math]
>[math]\frac{3}{3} > 0.\bar{9}[/math]
Blue is just not even math and is bullshit

>>9726352
[math]0.\bar{9}[/math] is shorthand for repetitive 9's you goofy nigger. Stop making up retarded bullshit and kys.
What faggot country did you grow up in where you weren't taught fucking basic division.

>>9592858
I dunno nigger. Maybe by not using limits and actually knowing how to at least do 3rd grade math.

If you cant understand that 1/n becomes a smaller and smaller result as n increases as a number, and can't make the assuming leap that if such a greatest number were to exist as infinity, the result of 1/infinity would be the closer to zero than any real number n. You dont need limits to do fucking toddler math.

>>9563008
You are reading too far into repeating decimals bro.
They exist simply as a byproduct of concatenating long division, but designed by retards who never figured it'd make more sense to write the remainder instead.

0.999... is not 1

There cannot ever exist an infinite amount to have been fully counted to completion, thus there cannot ever exist an infinite amount, thus any arbatrarily large amount must be finite, and any arbatrarily large finite real number amount can be bounded by proper rules not abused by brainlets.
0.999... itself makes no sense unless you imply the 3 dots have a static, constant definition, else you're required to supply how much decimal accuracy you're going for.

X= 0.999...
10X = 9.99...
10X-X = 8.99...1
9X = 8.99...1
9X/9 = 0.999...
This is how normal people do normal that that actually matters

What is 1 ÷ 3?
Well 3 goes into 1 zero times
0.
But 3 goes into 10 three times
0.3
with one leftover, bring down a zero, into ten
0.33
With one leftover... bring down a zero, into a ten
0.333
With one left over....
0.3333
With one left over......
0.333333333
No matter how many 3's exist in this decimal, it will never fully equate the decimal value of [math]\frac{1}{3}[/math], so in reality [math]0.\bar{3} < \frac{1}{3}[/math], multiply it by 3, [math]0.\bar{9} < 1[/math]

>>9540030
You apparently missed learning division in elementary school is what you meant to say.
>m-muh /pol/ bogeyman