Standard form

Leaving the front number $\ge 10$, e.g. writing $52 \times 10^{145}$ instead of $5.2 \times 10^{146}$ — you must rewrite $52$ as $5.2 \times 10$ and add $1$ to the power.

Forgetting the carried power (e.g. $5.2 \times 10^{144}$) or getting the sign wrong ($5.2 \times 10^{-146}$).

Writing $5.2^{146}$ instead of $5.2 \times 10^{146}$ — the power belongs to the $10$, not to $a$.

To add or subtract, first make the powers of $10$ equal (or write both as ordinary numbers). $6 \times 10^8 + 7 \times 10^7$ is NOT $13 \times 10^{15}$; rewrite $7 \times 10^7 = 0.7 \times 10^8$ to get $6.7 \times 10^8$.

Converting to or from standard form, count the places carefully: $0.00032 = 3.2 \times 10^{-4}$ (four places), and a number less than $1$ gives a NEGATIVE power. Miscounting the zeros, or getting the sign of the power wrong, changes the answer by a factor of ten.