用10进制小数不能精确表示某些三进制小数

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用10进制小数不能精确表示某些三进制小数0.1(3)=0.33333333333……(10)
同理，用二进制小数也不能精确表示某些10进制小数。

C/C++ code
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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <locale.h>
int main() {
    float f;
    double d;
    char bs[65];
    char b[65];
    char s[80];
    unsigned char *p;
    char e[12];
    char *t;
    int ex;
 
    while (1) {
        printf("Input a float point number:");fflush(stdout);
        rewind(stdin);
        fgets(s,80,stdin);
        if (1==sscanf(s,"%f",&f) && 1==sscanf(s,"%lf",&d)) break;
    }
    printf("f=%g\n",f);
    p=(unsigned char *)&f;
    printf("hex=%02X %02X %02X %02X\n",p[3],p[2],p[1],p[0]);
    ltoa(*(long *)&f,b,2);
    sprintf(bs,"%032s",b);
    printf("bin=%s\n",bs);
    printf("bin=%.1s %.8s   %s\n",bs,bs+1,bs+9);
    strncpy(e,bs+1,8);e[8]=0;
    ex=strtol(e,&t,2);
    printf("    %c %-4d-127 1.%s\n",(bs[0]=='0')?'+':'-',ex,bs+9);
    ex-=127;
    printf("    %c %-8d 1.%s\n",(bs[0]=='0')?'+':'-',ex,bs+9);
 
    printf("\nd=%lg\n",d);
    p=(unsigned char *)&d;
    printf("hex=%02X %02X %02X %02X %02X %02X %02X %02X\n",p[7],p[6],p[5],p[4],p[3],p[2],p[1],p[0]);
    _i64toa(*(__int64 *)&d,b,2);
    sprintf(bs,"%064s",b);
    printf("bin=%s\n",bs);
    printf("bin=%.1s %.11s   %s\n",bs,bs+1,bs+12);
    strncpy(e,bs+1,11);e[11]=0;
    ex=strtol(e,&t,2);
    printf("    %c %-6d-1023 1.%s\n",(bs[0]=='0')?'+':'-',ex,bs+12);
    ex-=1023;
    printf("    %c %-11d 1.%s\n",(bs[0]=='0')?'+':'-',ex,bs+12);
 
    return 0;
}
//Input a float point number:0.125
//f=0.125
//hex=3E 00 00 00
//bin=00111110000000000000000000000000
//bin=0 01111100   00000000000000000000000
//    + 124 -127 1.00000000000000000000000
//    + -3       1.00000000000000000000000
//
//d=0.125
//hex=3F C0 00 00 00 00 00 00
//bin=0011111111000000000000000000000000000000000000000000000000000000
//bin=0 01111111100   0000000000000000000000000000000000000000000000000000
//    + 1020  -1023 1.0000000000000000000000000000000000000000000000000000
//    + -3          1.0000000000000000000000000000000000000000000000000000
//

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