Let"s to speak you have two numbers. For this example, it can be 24 and also 25. Now, together I understand it, there have the right to be decimal intervals between them, such as 24.2, 24.34 and also even 24.788843.

You are watching: Decimals that have a finite number of digits

Now, what I"m wondering is:

Is over there the potential for an infinite number of decimal places? e.g. Would certainly it be feasible to continue adding much more decimal areas indefinitely, such together in the sample below?

24.8877544

24.88775443

24.887754438

24.8877544386

And for this reason on...

If there was, the would imply an unlimited quantity of numbers can be generated, without ever before reaching 25. And also if it that is the case, what sort of operation can be applied to produce such a pattern?

Thank you an extremely much!  Is there the potential for an infinite number of decimal places?

No potential around it. There are an infinite number of decimals.

Consider the simple duty $f(n)=25\times\fracnn-1$as $n$ goes come infinity. The will strategy $25$ but never acquire there.  Did you understand $1/3 = 0.33333\ldots$ through a $3$ recurring infinitely?

Actually you deserve to append any succession of digits to $24.$ to obtain numbers in between $24$ and $25$. And also if friend append an limitless sequence that nines, you"ll gain $24.9999\ldots = 25$. More numbers have infinite decimals expansions than execute not. You may have heard that the expansion of $\pi = 3.1415....$ go on forever and never repeats. In spite of what friend hear top top pi day, that is one of the least amazing things about pi as virtually all numbers have expansions the go on forever without repeating.

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And there"s no require to discover a "pattern". Any feasible sequence of numbers will certainly make a decimal number. Therefore I might take the number 24.429385.... And just begin typing number at random forever and it will certainly be a number.