Can 2 + 2 ≈ 5 be true? I was wondering a little, about how to proof that 2+2 =5 
And here I am: 
2.4 + 2.4 = 4.8
If we approximated numbers in each side individually then :
2 + 2 ≈ 5 
I know this may not be right, but I don't know why it's wrong. 

When you are talking about approximations you are usually doing so in a real world context. And so whether or not $4 \approx 5$ will depend on what you are measuring.
For example, the distance from the earth to the moon is $239,000$ miles. This is approximately equal to $240,000$ miles. So there $1,000$ is basically equal to zero. (That is $9,000$ is approximately $10,000$.)
But if I am on a road trip then $1,000$ miles is definitely not approximately equal to zero.
