Assume the decimal starts recurring immediately after the decimal point. (If the recurring string starts after k digits, then you want to find the (2001-k)th digit instead.)
Find the length of the recurring string = L
Find the remainder when 2001 is divided by L = R
The 2001st digit is the Rth digit in the recurring string.
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To find the 2001st digit in the repeating decimal for 1/7, we need to understand that 1/7 is a recurring decimal with a repeating pattern of 142857. Since the pattern length is 6 digits, we divide 2001 by 6 to get the remainder, which is 1. Therefore, the 2001st digit in the repeating decimal for 1/7 is the first digit in the repeating pattern, which is 1.
A decimal is a way of representing a number in such a way that the place value of each digit is ten times that of the digit to its right. A decimal representation does not require a decimal point. A decimal is not a sequence and so there is no nth term in a decimal.
In general, to compare decimal numbers, first compare the whole part. If those are the same, compare the first digit after the decimal point. If those are equal, the second digit, etc., until you find a digit that is different.
Just compare the digits one by one: compare the first digit after the decimal point with the first digit of the other number, the second digit with the second digit, etc., until you find a digit that is different.
Since the whole part is the same, compare each of the decimal digits (compare the first digit with the first digit, the second digit with the second digit, etc.), until you find a pair that is different.