need help understanding output after using setprecision.

[worn wraith]

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[rain spoke]

in C++ the floating point types can represent a limited amount of significant numbers with precision. the limit is decided by the IEEE-754 floating point representation.

The first output is a number with float type, a float supports a precision up to 6-9 numbers, typically 7.. that means It'll always represent the first 6 numbers accurately, and it may represent up to 9. but It usually represent accurately up to 7

the second output is a number with double type, a double supports a precision of siginifcant digits up to 15-18, typically 16

Although I don't know why we're limited in the first place, perhaps someone who's more knowledgeable than me will explain it

[calm lynx]

Thank your for your response, isn't the point of setprecision() to adjust the precision of float? Why does it not extend it beyond 6 even after setting it as far as 17?

[fluid creek]

It's just to set precision as in float converted to text can have as far as N literals after ., not the precision of the float itself

[rain spoke]

No, you do not adjust the precision of "float", instead you adjust the precision of the output

by default the output cannot be accurate for more than 6 signifcant digits "even if you used double"

[fluid creek]

number.N_literals_set_by_setprecision

and since float can store only range of numbers, it cannot magically figure out what are next literals, let's say to infinity

it does not calculate further what float would store

[calm lynx]

ohh ok my bad, i didnt have my concepts clear

how does the language determine what numbers are put in after 6 numbers?

i dont think its randomized as it gives the same output everytime

[fluid creek]

This stems from the fact how we store floating point numbers/fractionals.
float and double have their own representation, one cannot simply read the number as would int.
What we really store is aproximation of a number, usually a pretty good approximation, that allows us to also store numbers that supposedly would need infinite memory after ., infinite decimal expansion (does not really let us to go to infinity per se)?
We methodically store information required to get the actual number as human usually would write it, if needed.
That also allows us to figure out where the . should be placed.
https://en.wikipedia.org/wiki/Floating-point_arithmetic

Here you have possible maximum values for different primitive types:
https://en.cppreference.com/w/cpp/types/numeric_limits