# Amaqhezu edesimali1121

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.

Emva