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What is the hundredth digit after the decimal point when the fraction is written as a decimal?
Full solution
Q. What is the hundredth digit after the decimal point when the fraction is written as a decimal?
- Convert to Decimal: To find the hundredth digit after the decimal point for the fraction , we need to divide by to convert the fraction into a decimal.
- Perform Long Division: Performing the long division of by , we get a repeating decimal. The division goes as follows: divided by equals , and then the sequence repeats indefinitely.
- Identify Repeating Sequence: We need to identify the hundredth digit after the decimal point. Since the sequence repeats every digits, we can find the position of the hundredth digit by calculating , which gives us the remainder of the hundredth position within the repeating sequence.
- Calculate Hundredth Position: Calculating gives us a remainder of . This means that the hundredth digit is the fourth digit in the repeating sequence .
- Find Hundredth Digit: The fourth digit in the sequence is . Therefore, the hundredth digit after the decimal point when the fraction is written as a decimal is .
