Grade School Math: Bad math, or new meanings? I came across this online quiz discussing the new Common Core education standards, and it all seemed pretty reasonable, until I came across this question:

In the number below, how many times greater is the number represented by the digit in the thousands place than the number represented by the digit in the hundreds place?

57,762

1,
10,
100,
1000

I answered "1", as the number represented by the digit in the thousands place is 7, as is the number represented by the digit in the hundreds place.
Yet, my answer was deemed incorrect.
It seems as though they interpret the "number represented by the digit in the thousands place" as 7000. I understand this interpretation, but this is not the definition of "digit" that I have used in 30+ years.
My question: Is this genuinely bad math, or did the meaning of "digit" change sometime along the way?

 A: The convoluted formulation "the number represented by the digit" instead of simply "the digit" should have made you frown. OK, you took the number represented by the digit if we write down the number that has exactly one digit (i.e. by the digit alone, with strict distinction between the digit $7$ and the  number seven), while they apparently wanted something like the contribution of the digit to the given number - which they maybe didn't say explicit enough.
Admittedly, this does not seem like a very interesting concept. Then again, someone checking your business plan and saying "you have an error in the thousands digit" may lead to more concern than someone  saying "you have an error in the hundreds digit". 
Additionally, I'd usually distinguish between "$n$ times as big as" and "$n$ times greater than", taking the latter to mean "$(n+1)$ times as big as". Conclusion: Language is a much more complicated issue than math.
A: Three different things: place value, value, and digit.
Both digits are $7$.
The digit with a place value of thousands has a value of $7000$.
The digit with a place value of hundreds has  a value of $700$.
I tutor and this is a really difficult thing to teach. That doesn't mean that it should not be taught though. Right now, books are disappearing and computerized education is taking over. It is going to take a while for a stable system to bubble up and for teachers to learn how to deal with it effectively. In the old days, I would have scolded you and told you to read the book. Now I suppose, I would suggest Kahn academy. The man could teach calculus to goats.
