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Conversely the period of the repeating decimal of a fraction c / d will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction 2 / 7 has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction 2 / 7 is ...
The latter fraction is the best possible rational approximation of π using fewer than five decimal digits in the numerator and denominator. Zu Chongzhi's results surpass the accuracy reached in Hellenistic mathematics, and would remain without improvement for close to a millennium.
This smaller form factor is similar to that used in an HDD by Rodime in 1983, which was the same size as the "half height" 3½" FDD, i.e., 1.63 inches high. Today, the 1-inch high ("slimline" or "low-profile") version of this form factor is the most popular form used in most desktops.
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