Ever wondered why the value of G in <PERSON>'s law of gravitation is not 1 just like in this case you stated. Keep reading. I will come to the answer a bit later.
This is <PERSON>'s law of Gravitation:
F =(G×m1×m2)/R²
In this equation, there are four "defined" physical quantities m1,m2, R and F . 1kg of mass is defined as the mass of platinum-iridium aloy kept in at the International Bureau of Weights and Measures at Serves near Paris, similarly length (R) is defined as the length of a platinum-iridium rod and F is defined by <PERSON>'s first law of motion: F=ma(have patience).
So knowing the rest of the four quantity in the equation the value of unknown G(the fifth quantity) can be determined easily(using a torsion balance).
But what to do if there are two unknowns as in equation of <PERSON>'s first law: F=kma Here k and F both are unknowns. When <PERSON> discovered the law, the unit of force was not defined. No one thought of measuring forces. So F is also an unknown value in the equation. But it does contains F, so it can be used to define F instead! So <PERSON> got an equation which he could use to define the first ever unit of force. But what to do of that constant k? Why was it chosen as 1?
In fact, the value of k can be any real number but IUPAC took it as 1. 651
Why? Because it was the easiest way. Taking k=1,the equation becomes F=ma. It is easy to say that 1 Newton of force is the force that can produce an acceleration of 1 m/s² to a body of mass 1kg. But we take k as 4.72675(any arbitrary number) we will have to include it in the definition. Also it will become measurements and calculations more difficult. So taking k as 1 is easier for us.
Now you can understand that had <PERSON> discovered his law of gravitation first, he would have used it instead to define the unit of force. In that case he would had taken G as 1. And then the value of k in his first law would been something else ( may be it would had been a complex value just as G). Now you can see that it's one because it makes it easy. 439