Rome for the day from Florence

You can buy on the spot at the station if you want and the one way full price (Base fare) on standard class (the most economical) is 45€.
But if you buy early online (sales start 120 days prior) you can save a lot on a SuperEconomy fare. Be aware however that the SuperEcononmy and Economy fares are non refundable and not changeable therefore once you book seats on a specific train at those fares you can't change it anymore. So you must be certain about your travel plans if you want those discounted fares. Go to:
www.trenitalia.com for timetables, pricing and for pre purchase. The station names in Italian are:
FIRENZE SANTA MARIA NOVELLA
ROMA TERMINI
There are 3 to 4 high speed trains per hour in each direction from early morn to night, so plenty of choices.

There are certain times of the year that Trenitalia posts the updated schedule and rates for the next time period, I think it's every 6 months, but another poster will correct me if I'm wrong about the time period. For my most recent trip from Florence to Rome, October 14, I purchased and printed the tickets in August. But I knew the exact day and time of the train I needed to take because these tickets are nonrefundable.

It's been a few years (2013), but on our last trip to Italy we happened upon 2 for 1 weekend (or maybe it was Sunday only ... having a senior moment here) fares on the frecciargento and frecciarossa routes between Florence and Rome, for tickets purchased about a week in advance. Not sure if they're still being offered but you might want to do some comparison shopping on the trenitalia website using different dates to see if it makes any difference.

You are not forced to travel with trenitalia. You can use also one of Italotreno's high speed trains. www.italotreno.it/en .

Italotreno is a private competitor that runs its own trains on high speed routes. Their prices can be better than trenitalia's.

The 2-for-1 and same day roundtrip fares are usually not as good as the super-economy fares, in my experience.

If you can, try to leave as early as you can so that you can have a quick coffee upon arrival and then off to Piazza Navona, Trevi Fountain, Piazza di Spagna, Roman Forum, Coliseo, a few churches, Trastevere.
enjoy a nice lunch, maybe a pizza, Roman pizzas are delicious with a thin and crispy paste, unlike Napoli pizzas.
Or maybe you would prefer visiting the Vatican? I do not think you could do both but both deserves a visit.
I think latest Trenitalia train from Rome to Florence is around 8 pm from Termini Station.
Enjoy your day in Rome and come back to Rome for a week another time.
At least you'll get the flair.
Both 2 for 1 and super economy are very good values but there are less super economy fares available than 2for 1. Check what is best for you.