Dear GreenWhiteBlue: We are divided by our language. In BE usage "and" is essential, to omit it is presumably absolutely correct American English.Assuming you are writing this on a check, it would be two hundred thirty-four and 45/100 dollars.
It is "two hundred", not "two hundreds".
There is no "and" between the "two hundred" and the "thirty-four".
"Thirty-four" is written with a hyphen.
When writing the number 234.45 on a check, you would do this regardless of whether the amount was in dollars, or pounds, or euros, or any other decimal currency.