8. Aisha writes down all the numbers from 1 to 2020. What is the difference between the number of "1" digits and the number of "0" digits she has written?
(A) 78
(B) 1010
(C) 1089
(D) 2020
(E) 5005
8. The answer is (C). We observe that, given a number with decimal notation $a b c d$, if we fix $a \neq 0$, we have 10 choices for each of the digits $b, c, d$: among these 10 choices, exactly one is "1", and exactly one is "0". We also note that the same reasoning can be applied to a three-digit number $a b c$ and a two-digit number $a b$.

This allows us to say that, if $a \neq 1$, the number of "1"s and "0"s between $a 000$ and $a 999$ is the same; if instead $a=1$, we will have 1000 "1"s (from the digit $a$ written a thousand times) more than "0"s.

Similarly, if $a \neq 1$, the number of "1"s and "0"s between $a 00$ and $a 99$ and between $a 0$ and $a 9$ is the same. If instead $a=1$, we have 100 "1"s more between 100 and 199 and 10 "1"s more between 10 and 19.

Let $\Delta N$ be the difference between the number of "1"s and the number of "0"s in the set of numbers $N$. We can then state that:

- For $N_{1}$, the set of numbers between 1 and 9, we have $\Delta N_{1}=1$;
- for $N_{2}$, the set of numbers between 10 and 19, we have $\Delta N_{2}=10$;
- for $N_{3}$, the set of numbers between 20 and 99, we have $\Delta N_{3}=0$;
- for $N_{4}$, the set of numbers between 100 and 199, we have $\Delta N_{4}=100$;
- for $N_{5}$, the set of numbers between 200 and 999, we have $\Delta N_{5}=0$;
- for $N_{6}$, the set of numbers between 1000 and 1999, we have $\Delta N_{6}=1000$.

It only remains to count $\Delta N_{7}$ with $N_{7}$ being the set of numbers between 2000 and 2020, but it is easy to verify that $\Delta N_{7}=-22$. Therefore, if $N$ is the set of all numbers between 1 and 2020, $\Delta N=\sum_{i=1}^{7} \Delta N_{i}=$ $1111-22=1089$.