The expression cannot be written?

Question

I am solving exercises, and I found this one. The problem is that my result was:

$2 * 10^{-9}$ , but this answer not appear in the alternatives, what is wrong ?

Answer 1

Rewrite everything in terms of scientific notation:

$${4 \cdot 10^{-3} \over 2 \cdot 10^{-4}} \times {6.4 \cdot 10^{-4} \over 1.6 \cdot 10^6}$$

Then divide, coefficient by coefficient and powers of ten by powers of ten. Division means the subtraction of powers, yielding:

$${2 \cdot 10^{-3-(-4)}} \times 4\cdot 10^{-4-6} = 8\cdot 10^{1+(-10)}=8\cdot 10^{-9}$$

Answer 2

Here's a sanity check: forget about the scientific notation, and you have $$\frac{4\cdot 64}{2\cdot 16}=\frac{4\cdot 64}{32}=4\cdot 2=8$$

Hence your answer of $2$ cannot be correct. If some of the options did not have an $8$, you could eliminate those immediately. However, since they all begin with $8$, you must now worry about the scientific notation.