# Nā hakina decimal1121

Ua kapa ʻia nā helu decimal palena he mau hakina decimal, no ka mea, he hōʻike ʻokoʻa lākou no nā hakina me nā mana he ʻumi ma ka denominator. Pela no:

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

me $$k \in \mathbb{N}$$ a me $$q_k$$ ka $$k-1$$ -th wahi ma ka akau ma hope o ke koma.

I kēia manawa:

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

'O ia ho'i: Inā hiki ke ho'onui 'ia ka denominator i $$2^k \cdot 5^k$$ no ka hakina ma'amau i loko o ka 'ano pōkole loa $$\frac{z}{n}$$ , he hakina pauka hope. . Inā mākou e noʻonoʻo i ka helu kumu nui o ka denominator $$n = p_1^{l_1} \cdot \, \dots \, \cdot p_j^{l_j}$$ , a laila e like me ka theorem kumu o ka helu helu, hiki ke hōʻike ʻia kēia me he mea lā. $$f = 2^{km} \cdot 5^{kn}$$ i $$2^k \cdot 5^k$$ ina $$n = 2^m \cdot 5^n$$ . Pili kēia:

ʻO nā hakina wale nō i loaʻa ʻole nā ​​helu kumu kumu ma mua o nā 2 a i ʻole 5 i ka wā i hoʻopau piha ʻia e hoʻopuka i kahi hakina decimal palena.

Hope