setprecision（）的固定功能很粘

Question

#include <iostream>
#include <iomanip>
int main() {
    float a = 456.123456789;
    std::cout << a << "\n"; //State 1
    std::cout << "fixed " << fixed << a << "\n"; //State 2
    std::cout << a << "\n"; //State 3
}

输出：

456.123 //State 1
fixed 456.123444 //State 2
456.123444 //State 3

我想要做的是切换回状态1，那我该怎么做呢？我尝试了一些基于http://www.cplusplus.com/reference/iomanip/setprecision/的事情，但都失败了。