To multiply decimals using the standard algorithm, ignore the decimal point at first and multiply as if there were no decimal. Then count the total number of digits after the decimal point in both numbers combined. Place the decimal point in the product that many places from the right end.
To divide decimals using the standard algorithm, convert both numbers into whole numbers by multiplying them by powers of 10. Multiply both dividend and divisor by the same power of 10. Then divide as you would with whole numbers, placing your decimal point in the quotient accordingly.
Reasoning and estimating before calculating helps students develop critical thinking skills. It allows them to make informed decisions about whether their answer is reasonable or not. Estimating can also help students catch errors early on and save time during calculations.