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Decimals
Coins are often used to express a fraction of a currency. In the US, a quarter is $0.25 and a dime is $0.10. Counting change is just one of many ways you can put decimals to use in everyday life.
In the infinite series
\[ \frac { 1 }{ 9 } +\frac { 1 }{ 99 } +......+\cfrac { 1 }{ { 10 }^{ n }-1 } + \ldots \]
at what place after the decimal point does the third 1 occur?
Note: The first 1 occurs at the first place after the decimal point.
Inspired by this problem
by
Ayush Garg
\[0.\overline{0009182736455463728191}=\frac{1}{N}\]
Given that \(N\) is a 4-digit integer, find \(N\).
Note: The repeated digits are from 00, 09, 18, ..., 81,(those multiple 9), followed by 91, the period is 22.
by
Chan Lye Lee
Consider the following series written in form of a decimal \[A = \frac{1}{9} + \frac{1}{99} + \frac{1}{999} + .... + \frac{1}{10^{100} - 1}\]
Find the digit in the \(71\)st place after the decimal point.
by
Eddie The Head
\[0.\overline{00010203040506\ldots 969799}=\frac{1}{N}\]
Given that \(N\) is a 4-digit integer, find \(N\).
Clarification: The repeated digits are from 00, 01, 02, ..., till 99, without 98, the period is 198.
by
Chan Lye Lee
What is the \(1000^\text{th}\) digit to the right of the decimal point in the decimal representation of \((1+\sqrt{2})^{3000}\)?
by
Ayush Rai