int main(){

int miles;

do{
cout<<"Input your miles: ";
cin >>miles;
if (miles == 1.609){
cout<<"1 mile." <<endl;
}
else{
cout <<"\nDistance is " << convert(miles) << " km." <<endl;
}
}while(miles > 0) ;
return(0);
}

when i input 1.609 i get an infitine loop that continues until i manually close the program

What if you get rid of the If, and instead converting in Else, just Convert whatever the user inputs?

Besides, why are you using a loop?
I think you just need to do the procedure once, you could use a loop when asking the user if he'd like to convert a different measure...
Hmn?

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Mi-Re-Do-Re-Mi-Fa-Mi.