What is the 2012th digit after the decimal point in the decimal expansion of 8/81?
To find the 2012th digit after the decimal point in the decimal expansion of 8/81, we can follow these steps:
Step 1: Calculate the decimal representation of 8/81
To obtain the decimal representation of any fraction, you need to perform long division. In this case, divide 8 by 81.
0.098765432098765432...
Step 2: Determine the pattern
In this case, we can see that there is a repeating pattern of digits after the decimal point. The pattern repeats every 81 digits.
Step 3: Find the position of the 2012th digit
To find the position of the 2012th digit, divide 2012 by the length of the repeating pattern (81) and take the remainder.
2012 รท 81 = 24 remainder 68
Step 4: Locate the digit
The remainder (68) represents the position within the repeating pattern. Therefore, the 2012th digit after the decimal point is the 68th digit in the repeating pattern.
The 68th digit is 8.
So, the 2012th digit after the decimal point in the decimal expansion of 8/81 is 8.