#include<iostream>
#include<cstdio>
#define N 50000
using namespace std;
long long read()
{
    char c=0;
    long long sum=0;
    while (c<'0'||c>'9') c=getchar();
    while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
    return sum;
}
__int128 T,a,b,sx,sy,n;
double ans;
__int128 gcd(__int128 a,__int128 b)
{
    if (!b) return a;
    return gcd(b,a%b);
}
__int128 lcm(__int128 a,__int128 b)
{
    return a/gcd(a,b)*b;
}
void exgcd(__int128 a,__int128 b)
{
    if (!b)
    {
	sx=1,sy=0;
	return;
    }
    exgcd(b,a%b);
    __int128 tx=sx;
    sx=sy,sy=tx-(a/b)*sy;
    return;
}
int main()
{
    __int128 d=0,p=1,sp,g;
    T=read();
    while (T--)
    {
	a=read(),b=read(),g=gcd(p,b),sp=lcm(p,b);
	if ((a-d)%g!=0)
	{
	    puts("error");
	    return 0;
	}
	exgcd(p,b),sx=((sx*((a-d)/g))%sp+sp)%sp,d=(p*sx+d)%sp,p=sp;
    }
    n=d;
    if (n<2)
    {
	puts("error");
	return 0;
    }
    if (n==2) ans=1.0/2;
    else if (n==3) ans=2.0/3;
    else ans=5.0/8;
    printf("%0.6lf\n",ans);
    return 0;
}