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In March 26 speech in Warsaw Biden claimed that "it takes about 200 rubles to equal one dollar". In reality, the onshore USD/RUB closed at 96.0, whereas offshore USD/RUB closed at 102.29.
Moreover, Biden said that "the economy is on track to be cut in half in the coming years". This seems to be a highly unconventional estimate, e.g. J.P.Morgan estimates that "A peak-to trough decline in Russian GDP is now expected at around 12%".
So, why were Biden's remarks so inaccurate?
About rubles.
On March 9, currency exchange was prohibited in Russia. Ordinary people cannot legally exchange rubles to dollars or euros in Russia. They can withdraw up to $10,000 per person from their bank accounts (only dollars, not euros), providing the bank account is in foreign currency. But it was not always easy in practice, as many customers started to withdraw dollars simultaneously, which caused the shortage of cash in banks. Besides, only 10% of Russians had $10,000 or more in their foreign currency accounts, and many had no foreign currency accounts at all.
As a result, the black market of dollars and euros emerged. Initially, the prices at the black market were as high as 200 roubles per dollar or 350 roubles per euro (as people could withdraw dollars, but not euros). Other people went to Minsk or Helsinki to exchange rubles. The prices were as high as 270 rubles per euro in Helsinki or 300 roubles per euro in Minsk.
As for March 20, the prices dropped. Those who wanted to withdraw $10,000 or less, received the money, and the black market prices dropped to 110-120 rubles.
That's where Biden got the "200 rubles per dollar" figure.
One of the 'jobs' of a President is to be an inspirational figure. This goes all the way back to the Founders, who created the Presidency because they thought people were too accustomed to authority figures: if they didn't have a leader they could turn to, they might rise up and install one. Some presidents do it better, some do it worse, some pervert the principle entirely, but that's as may be...
Being inspirational is an act of rhetoric: it relies on authenticity and dramaturgy, not reasoned analysis. Inaccuracy is one of the prices paid for connecting with people on an emotional level. No one has all the facts in their head, and in a moment of trying to stir people a quick and dirty (even exaggerated) estimate is more useful than a mood-breaking pause to get things right.
This is (incidentally) one of the weaknesses of Liberal democracy in general and US democracy in particular. Some people are willing to abandon all facts and all intellectual accountability, and use rhetoric to maintain a constant state of emotional arousal. That can be an effective political tactic in the short term, but it ultimately destroys faith in the democratic system and trust in elected leaders. That often brings tyrannical rule in through the back door.
This is somewhat speculative, but if you look carefully at the video of the speech, he appears to go on a little improv and not actually be reading from the glass teleprompters (located the sides) when he gave the exchange rate. So I think we can mostly exclude that he might have had a bad speech writer on that specific issue.
And it appears that the 200 roubles/USD is a repetition of an older line of Biden. According to the NY Post, he said exactly the same thing on March 11, "to a conference of House Democrats in Philadelphia". The rouble was lower then, but arguably not that low, at least on the official markets (114 in Moscow, 125/135 on Refinitiv. It had also hit an intraday low of 132 even in Mosow, on the day before.)
It's worth recalling that the White House has been forced to issue some level of corrections lately to Biden's unscripted remarks, most notably on Putin being a war criminal and to "cannot remain in power". The latter remark appears to have been delivered in the same speech in Poland as the most recent 200 exchange rate claim, by the way. I guess the exaggerated exchange rate didn't elicit enough pushback or questions from the press (or for Moscow), for the White House to correct Biden on that talking point (now or on March 11).
As for the future predictions on the Russian economy... Well, Biden wasn't exactly precise on the time frame. If sanctions stay in place 50 years like for North Korea or Cuba... who knows. But yeah, that's an extreme scenario. That technique is pretty common in politician's speeches, by the way: present some extreme future scenario without caveats. You'll note that Putin does the latter too, e.g. claim NATO is going to put hypersonic missiles in Ukraine, or that Ukraine was going to acquire nuclear weapons with Western help. All predicted to happen at some rather unspecified point in the future.
And some sources like IFW Kiel put Russia's GPD growth at about -10% per year, long term following a decoupling of sort from the West. If that were true, it would take only 7-8 years for a 50% drop from the current GDP. N.B. that model "simulates a doubling of non-tariff trade barriers, but does not model the recently adopted sanctions against Russia."
It's generally hard to accurately answer a "why" question without being that person, but in this case there are obvious reasons to give false statements. In an ongoing conflict, leaders (etc.) will generally make false statements to influence public opinion towards a certain extreme (technical term is propaganda).
Another, unrelated reason to do so was popularized during the 2016 US presidential election: to make an outlandish claim so people would be motivated to research the issue in question to prove the claim wrong (essentially calling attention to a certain area). Though I cannot imagine why the POTUS would want to call attention to the value of the ruble.
