I'd just like to give more accurate information. This is from Viz translation of the manga, so it has little more bearing than the fan translation used by OP.
Gotenks actually states he travelled the globe a few dozen times. Dozen = 12, Few is anything greater than 2. For the bear minimum that's 36 times.
If you take the diamter of his trips for all 5 shown laps and compare them with that of the earth you will get these values.
Perimeter of orbit 1: 82,211 km
Perimeter of orbit 2: 75,098 km
Perimeter of orbit 3: 62,361 km
Perimeter of orbit 4: 56,406 km
Perimeter of orbit 5: 44,827 km
That's an average perimeter of 64180 km, multiply that by 36 for bear minimum and that's 2,310,501.6 KM
Now here comes the tricky part how much is a Nap really. Well if we use the anime for our unknown time T in this video we see Gotenks takes roughly 9 secs to make 9 loops, that means that it would take him 36 secs to complete 36 loops.
Start video at 2:57 sec
Thus, (2,310,501.6 x 10^3) m/36 sec = 64180600 m s^-1
Speed of sound is 340 ms^-1 which is equal to mach 1.
This puts Gotenks travelling speed at Mach 188,766. Speed of Light in vaccum is 881,000 Mach. That puts gotenks travelling speed for the minimum at 0.21 Speed of Light, If goes SSJ2 this would increase to 0.42, and SSJ 3 3.42 Speed of light. Evidence of this comes from Super exciting guide which gives the exact multiplier of the SSJ transformation. This is the minimum speed of gotenks assume that a few means 3, if its higher so to will this number.
Lastly, I'd just like to point out this isn't his top speed as evident by him saying "I'm sure the speed was proof enough" indicating he can go faster if need be.