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?
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.