In fact, I can also tell you that $~$\\log\_{10}(\\text{2,310,426})$~$ is between 6\.30 and 6\.48, because the seventh digit is worth more than a 2\-digit and less than a 3\-digit \(and I looked up the natural exchange rates for 2\-digits and 3\-digits in terms of 10\-digits\)\.
How about, "because I'm going to need six 10-digits to get up to a million, and something more than a 2-digit and less than a 3-digit to get from there to a number between 2 and 3 million."
I'm not sure that would be the right way to say it, but I still feel like the current text is problematic, because:
1) Whether you say last digit, or seventh digit, in either case I'm reading right-to-left and my first thought is that you're talking about the ones place.
2) Even if you said something like left-most digit, that wouldn't be right, because it's not that 2 is between 2 and 3, it's that the value of the whole number is greater than 210^6 and less than 310^6.
I think you're referring to a digit in an abstract sense that doesn't directly map to the digits we write down, so you may have to go out of your way to avoid confusing nth digit with a particular one of the numerals that are written above.