Izinombolo zedesimali eziphelele zibizwa ngokuthi amafrakhishini edesimali, ngoba ziwumfanekiso ohlukile wamaqhezu anamandla ayishumi kudinominetha. Kanjalo:

$$\frac{z}{n} = \frac{q_1}{1} + \frac{q_2}{10} + \dots + \frac{q_k}{10^k}$$

ngokuthi $$k \in \mathbb{N}$$ kanye $$q_k$$ $$k-1$$ -th indawo kwesokudla ngemva kwekhefana.

Manje kunjalo:

$$\frac{z}{n} = \frac{10^k \cdot q_1 + 10^{k-1} q_2 + \dots + q_k}{10^k} = \frac{10^k \cdot q_1 + 10^{k-1} q_2 + \dots + q_k}{2^k \cdot 5^k}$$

Lokhu kusho ukuthi: Uma idinominayitha inganwetshwa ukuze ithi $$2^k \cdot 5^k$$ engxenyeni evamile ngendlela efushanisiwe ngokuphelele $$\frac{z}{n}$$ , iyingxenyana yedesimali enomkhawulo. . Uma sicabangela i-factorization eyinhloko ye-denominator $$n = p_1^{l_1} \cdot \, \dots \, \cdot p_j^{l_j}$$ , khona-ke ngokusho kwe-theorem eyisisekelo ye-arithmetic, lokhu kungavezwa ngokuthi $$f = 2^{km} \cdot 5^{kn}$$ kuya $$2^k \cdot 5^k$$ uma $$n = 2^m \cdot 5^n$$ . Lokhu kuyasebenza:

Amafrakshini kuphela amadenominetha awo angenazo izici eziyinhloko ngaphandle kuka-2 noma 5 lapho isifinyezo esigcwele siphumela engxenyeni yedesimali enomkhawulo.

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