Question

0.34十进制成二进制是多少？

Answer 1

乘以2，取进位：
0.34×2=0.68，进0
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0.68×2=1.36，进1
0.36×2=0.72，进0
0.72×2=1.44，进1，
0.44×2=0.88，进0，
0.88×2=1.76，进1，
0.76×2=1.52，进1，
0.52×2=1.04，进1
0.04×2=0.08，进0
0.08×2=0.16，进0
0.16×2=0.32，进0
0.32×2=0.64，进0
0.64×2=1.28，进1
0.28×2=0.56，进0
0.56×2=1.12，进1
0.12×2=0.24，进0
0.24×2=0.48，进0
0.48×2=0.96，进0
0.96×2=1.92，进1
0.92×2=1.84，进1
0.84×2=1.68，进1
0.68×2=1.36，进1，开始另一个循环：
0.34的二进制为0.0101，0111，0000，1010，11...

也可以化成1/2^n的和：
0.34=34/100
=25/100+9/100
=1/4+36/400
=1/4+25/400+11/400
=1/4+1/16+44/1600
=1/4+1/16+25/1600+19/1600
=1/4+1/16+1/64+19/1600
=1/4+1/16+1/64+38/3200
=1/4+1/16+1/64+25/3200+13/3200
=1/4+1/16+1/64+1/128+13/3200
=1/4+1/16+1/64+1/128+26/6400
=1/4+1/16+1/64+1/128+25/6400+1/6400
=1/4+1/16+1/64+1/128+1/256+1/6400
=0.01010111...