Question

设A,B是自然数,且A小于10,如果B除于444等于0.3A73A7.,那么B等于多少?

Answer 1

0.3A73A7……

= 3A7×0.001001……

= 3A7 ×0.111111…… / 111

= 3A7/111 × 1/9

= 3A7/999

B ÷ 444 = 3A7 ÷ 999 两边同×111即

B ÷ 4 = 3A7 ÷ 9 即

9B = 3A7×4

B = 3A7×4/9

显然3A7含有因数9.根据被9整除的性质,3 + A + 7 = 10 + A 能被9整除,推得A = 8

B = 387 ×4 / 9 = 172