Amanani edesimali apheleleyo abizwa ngokuba ngamaqhezu edesimali, kuba amele amaqhezu ahlukeneyo anamandla eshumi kwidinomineyitha. Kunjalo ke:
$$\frac{z}{n} = \frac{q_1}{1} + \frac{q_2}{10} + \dots + \frac{q_k}{10^k}$$
nge \(k \in \mathbb{N}\) kunye \(q_k\) ne \(k-1\) -th indawo ekunene emva kwesiphumlisi.
Ngoku kunjalo:
$$\frac{z}{n} = \frac{10^k \cdot q_1 + 10^{k-1} q_2 + \dots + q_k}{10^k} = \frac{10^k \cdot q_1 + 10^{k-1} q_2 + \dots + q_k}{2^k \cdot 5^k}$$
Oku kuthetha ukuba: Ukuba idinomineyitha inokwandiswa ukuya ku \(2^k \cdot 5^k\) kwiqhezu ngokubanzi ngendlela efinyeziweyo ngokupheleleyo \(\frac{z}{n}\) , liqhezu lokugqibela ledesimali. . Ukuba siqwalasela i-prime factorization ye-denominator \(n = p_1^{l_1} \cdot \, \dots \, \cdot p_j^{l_j}\) , ngoko ngokwe theory ye-arithmetic esisiseko, oku kunokubonakaliswa njenge \(f = 2^{km} \cdot 5^{kn}\) ukuya \(2^k \cdot 5^k\) ukuba \(n = 2^m \cdot 5^n\) . Oku kuyasebenza:
Ngamaqhezu kuphela anedinomineyitha angenayo imiba ephambili ngaphandle kwee-2 okanye ezi-5 xa zifinyeziwe ngokupheleleyo ziphumela kwiqhezu ledesimali enomda.