Convert float to string with precision & number of decimal digits specified?

A typical way would be to use stringstream:

#include <iomanip>
#include <sstream>

double pi = 3.14159265359;
std::stringstream stream;
stream << std::fixed << std::setprecision(2) << pi;
std::string s = stream.str();

See fixed

Use fixed floating-point notation

Sets the floatfield format flag for the str stream to fixed.

When floatfield is set to fixed, floating-point values are written using fixed-point notation: the value is represented with exactly as many digits in the decimal part as specified by the precision field (precision) and with no exponent part.

and setprecision.

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For conversions of technical purpose, like storing data in XML or JSON file, C++17 defines to_chars family of functions.

Assuming a compliant compiler (which we lack at the time of writing), something like this can be considered:

#include <array>
#include <charconv>

double pi = 3.14159265359;
std::array<char, 128> buffer;
auto [ptr, ec] = std::to_chars(buffer.data(), buffer.data() + buffer.size(), pi,
                               std::chars_format::fixed, 2);
if (ec == std::errc{}) {
    std::string s(buffer.data(), ptr);
    // ....
}
else {
    // error handling
}

The customary method for doing this sort of thing is to "print to string". In C++ that means using std::stringstream something like:

std::stringstream ss;
ss << std::fixed << std::setprecision(2) << number;
std::string mystring = ss.str();

You can use C++20 std::format:

#include <format>

int main() {
  std::string s = std::format("{:.2f}", 3.14159265359); // s == "3.14"
}

or the fmt::format function from the {fmt} library, std::format is based on (godbolt):

#include <fmt/core.h>

int main() {
  std::string s = fmt::format("{:.2f}", 3.14159265359); // s == "3.14"
}

where 2 is a precision.

It is not only shorter than using iostreams or sprintf but also significantly faster and is not affected by the locale.