For a sale, a store owner reduces the price of a $$10$ scarf by $20\%$.  Later the price is lowered again, this time by one-half the reduced price.  The price is now
$\text{(A)}\ 2.00\text{ dollars} \qquad \text{(B)}\ 3.75\text{ dollars} \qquad \text{(C)}\ 4.00\text{ dollars} \qquad \text{(D)}\ 4.90\text{ dollars} \qquad \text{(E)}\ 6.40\text{ dollars}$
Solution 1
$100\%-20\%=80\%$
$10\times80\%=10\times0.8$
$10\times0.8=8$
$\frac{8}{2}=4=\boxed{C}$

Solution 2
The first discount has percentage 20, which is then discounted again for half of the already discounted price.
$100-20=80$
$\frac{80}{2}=40$
$40\%\times10=10\times0.4=4=\boxed{C}$