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.