Are both correct below?

Only the second is correct.

victoAre both correct below—with and without and?

Yes, and omit the apostrophe.

Why omit the apostrophe? The worth of “one hundred and fifty dollars” is “one hundred and fifty dollars’ worth”. The apostrophe is required here.

The apostrophe is not required here. Apostrophes are often omitted in common expressions.

victoWhy omit the apostrophe? The worth of “one hundred and fifty dollars” is “one hundred and fifty dollars’ worth”. The apostrophe is required here.

I don't think so.
Suit yourself; I am not going to try to convince you.

Of course it takes an apostrophe. Where else does the "s" sound come from in "one dollar's worth"? We don't say "one dollar worth".

Not asking you to convince me; it would be a waste of time. Your answer is incorrect. The apostrophe is required.

enoon We don't say "one dollar worth".
why not?

one dollar worth of ice cream
fifty cents worth of candy

It's not the same as 'one month's rent'.

From The Grammar Curmudgeon:

Another more common problem is the use of a possessive form when literal ownership is not involved. Here, we are still using the possessive shorthand as a substitute for the "of" or "for" phrase even though the situation does not involve true possession. Usually, this occurs with sums of money or periods of time. For instance, we refer to t

victoI rest my case.

Fine, rest your case. If you want to use unnecessary punctuation go ahead. I am not surprised that you found such a reference.

one hundred fifty dollars worth of merchandise

a dollar woth of candy

My point is that "worth of" already establishes the relationship between "fifty dollars" and "merchandi