Explain why you might want to write very large and very small numbers in scientific notation.

When you end up with very big numbers it simply becomes impractical! Take this as an example:

There are approximately 120 sextillion atoms in the universe (up to 300, but let's go with 120). Thats 120000000000000000000000 in decimal form. Put that in standard form (scientific form is the same thing I hope hehe), and you get 1.2*10^23. Much more practical.
Or, the diameter of a nucleus is 0.00000000000000175m, or 1.75*10^-15.

Basically, it just looks nicer and is far easier to compare to other numbers rather than counting zeros.