What is the 217th digit after the decimal point in the repeating decimal 0.3456? How can I calculate this?
Answer (3)
Well I think you mean 0. ( 3456 ) , I will try to explain as simple as I can ;p
First I would divide 217 by 4, because we need to find 217th digit in 4 digit repeating decimal:
217/4 = 4 217 = 54 4 1
54 4 1 it means that 3456 will be reapeted 54 times untill 217th digit, and 4 1 means that the 217th digit will be the first of those 4 digits in this decimal, so your answer is: The 217th number after the decimal point in this repeating decimal will be 3
To determine the 217th digit after the decimal point in the repeating decimal 0.3456, you need to recognize the pattern of the repetition and how it affects the position of each digit. The given decimal repeats every 4 digits, which means that the sequence 3456 will repeat itself over and over.
To find the 217th digit, divide 217 by the length of the repeating sequence, which is 4 in this case.
Divide the position number you're looking for, 217 in this instance, by the number of digits in the repeating block (4)
217 ÷ 4 gives you 54 with a remainder of 1.
The remainder represents the digit's position within the block. Since the remainder is 1, the 217th digit is the first digit in the repeating sequence of 0.3456
Therefore, the 217th digit after the decimal point is 3.
Note that while calculators can provide a long string of digits after the decimal point, those extra digits beyond the given significant figures of the original number may not have practical meaning, particularly when using numbers with a certain number of significant figures and performing different mathematical operations.
The 217th digit after the decimal point in the repeating decimal 0.3456 is 3. This is found by determining how many full cycles of the repeating segment fit into the first 217 digits and identifying the position within that segment. Since 3456 repeats every four digits, the first digit is 3.
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