I found out that 9 * 0.0001 = 0.0009000000000000001, but 9 / 10_000 = 0.0009

Is it guaranteed that when you divide by power of 10 you will receive exact value (by IEEE 754-2019: IEEE Standard for Floating-Point Arithmetic)

I am expecting someone who knows specific behavior of Floating-point standard to explain if there is such guarantees or not.

CodePudding user response：

0.009 cannot be represented precisely by IEEE 754 floating point. The binary representation of 0.009 would be:

0.0000001001001101110100101111000110101001111110111110011101101100100010110100001110010101100000010000011
     0001001001101110100101111000110101001111110111110011101101100100010110100001110010101100000010000011
     ...

It is a rational number with an infinite number of (binary) digits after the decimal point.

So this cannot be represented in floating point which only has a finite number of binary digits available in the mantissa part.

0.009 in floating point is represented as follows:

sign exponent    mantissa
0    01111000    00100110111010010111100

But as the binary sequence is finite here, it actually represents this number:

0.0089999996125698089599609375....

A similar deviation will occur for other positive powers of 10 in 9/10ⁿ

You can make the conversion using this tool.