close to vs approximately

close to and approximately both are adverbs.

Word	Noun	Adjective	Verb	Adverb
close to	No	No	No	Yes
approximately	No	No	No	Yes

As adverbs, close to and approximately are synonyms defined as:

close to and approximately: (of quantities) imprecise but fairly close to correct

Other synonyms of close to include about, around, just about, more or less, or so, roughly, some.

close to (adverb)	approximately (adverb)
(of quantities) imprecise but fairly close to correct	(of quantities) imprecise but fairly close to correct