Behaviour of setprecision in C++

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C++

double x = 3.14159;

	double y = 131.14159;

	double z = .00314159;

	double a = 13114.159;


	cout << setprecision(3) << "x =  " << x << endl;

	cout << "y =  " << y << endl;

	cout  << "z =  " << z << endl;

	cout  << "a =  " << a << endl;

What I have tried:

I am little bit confused about the behavior of setprecision. What I understand that setprecision tries to get the most significant digits before and after the decimal point (included) according to the value of precision. From my understanding,for the variable z it outputs .00314 because 314 are 3 most significant digits.I do not understand why for the last variable it outputs as 1.31e+04?