Question

把三進(jìn)制3121₍₃₎轉(zhuǎn)化為五進(jìn)制數(shù).

Answer 1

【探究】先把三進(jìn)制的數(shù)轉(zhuǎn)化為十進(jìn)制的數(shù),再把十進(jìn)制的數(shù)轉(zhuǎn)化為五進(jìn)制的數(shù).

【解】把3121₍₃₎轉(zhuǎn)化為十進(jìn)制數(shù)得

3121₍₃₎=3×3³+1×3²+2×3+1=97₍₁₀₎.

    把97₍₁₀₎轉(zhuǎn)化為五進(jìn)制數(shù)得

    故97₍₁₀₎=342₍₅₎,所以三進(jìn)制數(shù)3121₍₃₎轉(zhuǎn)化為五進(jìn)制數(shù)為342₍₅₎.

規(guī)律總結(jié) 由十進(jìn)制轉(zhuǎn)化為k進(jìn)制時(shí)方法為除k取余法,但要注意兩點(diǎn)：①除法要進(jìn)行到商0為止；②把余數(shù)從下到上依次排列才是所要求得的k進(jìn)制數(shù).