True or False?
Note: The "" indicates that there are infinitely many 9's.
Find the number of rational numbers such that when is written as a fraction in lowest terms, the numerator and denominator sum to 1000.
Recall that for example, stands for the repeating decimal and that the period of a repeating decimal is the number of digits in the repeating part. In this case, the period of is 2.
Find the sum of the periods of and .
Let represent the repeating decimal for . The product can be expressed as where are positive integers and is as small as possible. can be expressed as where are coprime integers. What is ?
Note: refers to the repeating decimal evalauted in base .
If the following infinite series is evaluated as a decimal,what is the 37th digit to the right of the decimal place?