Look closely at the binary representation for 77.1:

0100 0000 0101 0011 0100 0110 0110 0110
0110 0110 0110 0110 0110 0110 0110 0110

See how there's a lot of 0110 0110 0110 there at the end? That's because 0.1 has no exact representation in binary… it's a repeating binary number. It's sort of like how 1/3 has no representation in decimal. 1/3 is 0.33333333 and you have to keep writing 3's forever. If you lose patience, you get something inexact.

So you can imagine how, in decimal, if you tried to do 3*1/3, and you didn't have time to write 3's forever, the result you would get would be 0.99999999, not 1, and people would get angry with you for being wrong.