MHB 57^(th) digit in decimal expansion

juantheron
Messages
243
Reaction score
1
Calculation of $57^{th}$ digit in the decimal expansion of $\displaystyle \frac{1}{57}$
 
Mathematics news on Phys.org
jacks said:
Calculation of $57^{th}$ digit in the decimal expansion of $\displaystyle \frac{1}{57}$

If you are allowed mod calculation and Euler's phi function, you can use >>this<<.
It gives you the period of the decimal expansion, meaning it suffices to calculate a decimal that comes much earlier in the expansion.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

I On base-b expansion of nonnegative reals
Replies
7
Views
2K
B Can an infinite decimal expansion of a number repeat once?
Replies
15
Views
1K
I Non unicity of decimal expansion and extremes of intervals
2
Replies
54
Views
5K
MHB Solving for $k$: Digit Product = $\dfrac{25k}{8}-211$
Replies
2
Views
940
MHB A positive integer divisible by 2019 the sum of whose decimal digits is 2019.
Replies
2
Views
2K
Expansion Info-Representation With Arbitrarily Adjustable Decimals
Replies
2
Views
3K
I (0,1) is uncountable using binary expansions?
Replies
15
Views
2K
MHB Recreational Number Theory, Unsolved Problem
Replies
1
Views
2K
Multiple Decimal Expansions: Explained
Replies
2
Views
2K
MHB Converting Decimal to Hexadecimal for Compass Corrections
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top