Many authors and lecturers use the word approximate.

[blob100]

Many authors and lecturers use the word approximate.
It is not mathematically to say something is close to another...
I'm wondering what is the definition of approximate.

 

[Mark44]

See any dictionary for a definition of approximate.
There is usually nothing wrong with saying that two quantities are approximately equal, and the context will usually give you an idea of how close the approximation is. For example, the exact value of sin($\pi/4$) is sqrt(2)/2, or approximately 0.707. This approximation is accurate to three decimal places.