998, 001 and its Mysterious Recurring Decimals - Numberphile
video description
Formula for b-n is 1/(10-p-b) where p is precision and b is base
There are some approximations that I'd like to figure out a proper formula for
Be aware that they're most likely incorrect since I was really bored on a phone calculator and didn't bother too much about checking for errors
These follow n-2
1/96. 0692079. (0. 01 04 09 16)
1/996. 006992. (0. 001 004 009 016)
1/9996. 00069. (0. 0001 0004 0009 0016)
This one follows n-n
1/9995. 99889. (0. 0001 0004 0027 0256)
Date: 2022-04-08
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Comments and reviews: 9
Jason
I know this is an old video, but can you go through why 1/499 appears to be the powers of 2, in 3 digit increments (i. e. 0. 002004008016032? I'd love to see why that is true; a little different from sequential digits. It appears to do some overlap after' 064'. Tried it out with additional and reduced number of 9s and all seem to be variations with different significant places like your video here.
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I know this is an old video, but can you go through why 1/499 appears to be the powers of 2, in 3 digit increments (i. e. 0. 002004008016032? I'd love to see why that is true; a little different from sequential digits. It appears to do some overlap after' 064'. Tried it out with additional and reduced number of 9s and all seem to be variations with different significant places like your video here.
reply
Glider
I am happy for the internet to make this cool little fact so viral that Dr Grime explains it to me. The amazing fact is just awesome, but knowing the mechanism behind the fact is really cool.
I love the pause before he said the word 'formula' like it was something you should not say in a company of ladies.
And I could share his excitement when I made a division that ended with 0, 31415926
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I am happy for the internet to make this cool little fact so viral that Dr Grime explains it to me. The amazing fact is just awesome, but knowing the mechanism behind the fact is really cool.
I love the pause before he said the word 'formula' like it was something you should not say in a company of ladies.
And I could share his excitement when I made a division that ended with 0, 31415926
reply
John
They seem to have stumbled across what I call -Beck numbers-. That's where you take any whole number with an even number of digits, physically separate the two halves, add them, squaring it brings it back to the starting number. E. g, 81, 8+1, 9, squared = 81. 998001 happens to fall in this group. So does 99980001. There are only 15 under 10 billion.
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They seem to have stumbled across what I call -Beck numbers-. That's where you take any whole number with an even number of digits, physically separate the two halves, add them, squaring it brings it back to the starting number. E. g, 81, 8+1, 9, squared = 81. 998001 happens to fall in this group. So does 99980001. There are only 15 under 10 billion.
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Sailor376also
The sequence 142857, please note, and not dissimilar to your 998001 1/. 7 =. 142857142857, 2/7 =. 285714285714. 3/7 =. 42857142857142857. 4/7 =. 57142857142857,
all numbers divided by seven, everything to the right of the decimal point will always contain the sequence. 142857, repeated.
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The sequence 142857, please note, and not dissimilar to your 998001 1/. 7 =. 142857142857, 2/7 =. 285714285714. 3/7 =. 42857142857142857. 4/7 =. 57142857142857,
all numbers divided by seven, everything to the right of the decimal point will always contain the sequence. 142857, repeated.
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Deeksha
Ohhhhh so this is the reason for this! While doing a problem in electronics in class, I came across this fraction: 0. 0225/0. 018225 which gave 1. 23456790123. and then I wondered why 8 wasn't there. Finally got an explanation for it. Cool!
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Ohhhhh so this is the reason for this! While doing a problem in electronics in class, I came across this fraction: 0. 0225/0. 018225 which gave 1. 23456790123. and then I wondered why 8 wasn't there. Finally got an explanation for it. Cool!
reply
Artem
Did you notice that, if we take 997001 instead of 998001, and calculate 1/997001 = 0. 003008021055144. ? These are Fibonacci numbers, but not all of them. It's like each second one is skipped. Why does that happen?
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Did you notice that, if we take 997001 instead of 998001, and calculate 1/997001 = 0. 003008021055144. ? These are Fibonacci numbers, but not all of them. It's like each second one is skipped. Why does that happen?
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Paul
I know why.
I have demonstrated that to be a reurring sequence for the numbers 1 and 8.
Their recurring sequences are
123456790 and 790123456
Their ending sequences are
123456789 and
790123455
reply
I know why.
I have demonstrated that to be a reurring sequence for the numbers 1 and 8.
Their recurring sequences are
123456790 and 790123456
Their ending sequences are
123456789 and
790123455
reply
Nepali
Several years later. Same problem is viral again.
Everybody else be like it is something else this could be a big discovery,
Mathmaticians be like not again these idiots never learn do they.
reply
Several years later. Same problem is viral again.
Everybody else be like it is something else this could be a big discovery,
Mathmaticians be like not again these idiots never learn do they.
reply
Colbert
QUESTION: Would there be an advantage to create a number system using a prime base rather than base 10. For example, using base 11 or base 13 instead of base 10, which is not a prime number?
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QUESTION: Would there be an advantage to create a number system using a prime base rather than base 10. For example, using base 11 or base 13 instead of base 10, which is not a prime number?
reply
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