How many digits are in the repeating cycle of 1727?(1 point)
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To find the repeating cycle of a decimal representation, we can divide the number by a power of $10$. We have $1727 \div 10000 = 0.1727$. This means that the repeating cycle of $1727$ is the same as the repeating cycle of $0.1727$.
To find the repeating cycle of $0.1727$, we can set up a long division:
$$\begin{array}{c|cc} & 1727 & \\ \cline{2-3} 10000 & 0.1727 & \\ & -10000 & \\ \cline{2-2} & 727 & \\ & \vdots & \\ \end{array}$$
In the long division, we see that the remainder after dividing $727$ by $10000$ is $727$. This means that the repeating cycle of $0.1727$ (and therefore, the repeating cycle of $1727$) is $727$.
So, there is $\boxed{3}$ digits in the repeating cycle of $1727$.
To determine the number of digits in the repeating cycle of 1727, we need to find the \(d\) value in the decimal representation of the fraction \(\frac{1}{1727}\). The repeating cycle in a decimal representation occurs when we have a remainder that repeats.
To find the \(d\) value, we can use long division to divide 1 by 1727:
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1727 | 1 0.0006 11 47 867...
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2803
1727
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1076
1036
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40
0
The repeating cycle occurs when we get a remainder of 0. In this case, the repeating cycle is 11147. Therefore, there are 5 digits in the repeating cycle of 1727.