When multiplying decimals, how do you know where to place the decimal point? Think about this as you do parts (a) through (d) below.
a. Write two equations for multiplying 0.3 by 0.16. One equation should express the factors and product using decimals, and one using fractions.
b. In part (a), you multiplied tenths by hundredths to get thousandths. Do you always get thousandths if you multiply tenths by hundredths? Why or why not? What do you get if you multiply tenths by tenths? Hundredths by hundredths? Use several examples to justify your answers.
c. When a multiplication problem is written using decimals, there is a relationship between the number of decimal places in the parts (or factors) of the problem and the number of decimal places in the answer (or product). Describe this relationship.
d. Describe a shortcut for locating the decimal point in the answer to a problem involving decimal multiplication.