There was an article published on Coin Telegraph about three days ago that stated that with Bitcoin's limited supply cap, you only need 0.01 BTC to become filthy rich.

0.01 BTC is about $500, and there are different perspectives here, and in my opinion, I do not agree with this.
First, you consider, what exactly does it mean to be rich? Depending on how you view the concept of being "rich," then maybe for sure, 0.01 BTC will make you rich.
Will $10,000 make you feel rich because that is what 0.01 BTC will be worth when Bitcoin hits one million dollars one day, which we believe will happen one day. That means that when that happens, Bitcoin will have twice the market capitalization of gold.
So now, when that happens, will you be filthy rich with 10,000 dollars? Not really, by most people's standards, but can 0.01 BTC be worth a hundred thousand dollars?
Now the question is, will 100,000 dollars make you FILTHY rich? 100,000 is a lot of money, by the way, but it is not a filthy rich kind of money.
For 0.01 BTC to be worth a hundred thousand dollars, that means the market capital of Bitcoin would be worth 180 trillion dollars which is about 180x from the current price and the current market capital. This will be about twice the value of the entire global broad money supply which comprises every single money market account, every single banknote, every single saving, etc. The value of Bitcoin in that outline will be worth roughly 10 million dollars per coin, which is somehow unlikely for Bitcoin.
So now, to answer the question of how much Bitcoin you need to be filthy rich. If we are honest, if you have 0.01 Bitcoin, you have more Bitcoin thag most people have. But if you own 10BTC, that puts you in the super privileged class of Bitcoin holders.
Since addresses with ten or more Bitcoin represent a total of 0.36 percent of all Bitcoin holders, if you have one Bitcoin, you might probably be top 1.8 percent of Bitcoin global holders.
But the answer to the question is simply one Bitcoin. That is all you need, and even investing in Bitcoin at the current high price will still bring back significant returns. Bitcoin can indeed go up to a million dollars over time. It is only a matter of time.