Why can't a decimal 0.1 be a good representation of binary?

Binary notation ....

This is also the basic knowledge:

Don't worry about our 1.1-point explanation. Positive integer to binary, negative integer to binary, decimal to binary

Positive integer to binary: positive integers are converted to binary. Points must be sure to remember Kazakhstan: In addition to the second, and then the reverse order, high 0.

21/2-------------------------------1

10/2-------------------------------0

5/2-------------------------------1

2/2--------------------------------0

---------------------------------more than 1

Remember, to the sort 10101, verify that the next decimal is converted to: 1x2 's 4-square-+1x2 2-+1x2-square-=16+4+1=21. That's right.

The computer is generally 8-bit 16-bit 32-bit 64-bit, so not enough bit high to fill 0. 8-bit notation: 00010101

Negative integer to binary: first convert the corresponding positive integer into binary, reverse the binary, and then add one to the result.

Take-21 demo, see the formula,

The binary representation of 21 is: 10101

Reverse: 01010

Plus one: 01011

Decimal to Binary method: Multiply the number of decimal points by 2, have a result, take the integer portion of the result (not 1 is 0), and then multiply the fractional part by 2, then take the integer portion of the result ... And so on, until the number is divided into 0 or the number of digits is enough, OK.

Demo: 0.125x2=0.25 ......... ........ 0

0.25x2=0.5.............................0

0.5x2=1.0................................1

That is, 0.125 of the binary representation of the decimal part is divided into 0.001

Remember, multiply the decimal number to 0. Sort: Positive order.

Verification: 0.001 0x2 0-+0x2-1-square-+0x2-2-+0x2-3-square =1/8=0.125. Right.

Now to illustrate why the 0.1-turn binary cannot be represented:

0.1x2=0.2 ........ ........ 0

0.2x2=0.4 ........ ......... 0

0.4x2=0.8 ........ ........ 0

0.8x2=1.6.......................1

0.6x2=1.2.......................1

0.2x2=0.4.......................0

.....

is an infinite loop. So.... You know!

for (double i=0;i!=10;i+=0.1)
{
}

There could be a cycle of death. You need to pay attention to the floating point loop.

Why can't a decimal 0.1 be a good representation of binary?