Question

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.

Answer 1

a.Equation 1 \(\displaystyle{0.3}\cdot{0.16}\)
Equation 2 \(\displaystyle\frac{{3}}{{10}}\cdot\frac{{16}}{{100}}\)
b.\(\displaystyle\frac{{3}}{{10}}\cdot\frac{{16}}{{100}}={3}\cdot\frac{{16}}{{{10}\cdot{100}}}=\frac{{48}}{{1000}}\)
c.Multiply normally, ignoring the decimal points.
\(\displaystyle{3}\cdot{16}={48}\)
Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.
In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.
0.3 has 1 decimal places, 0.16 has 2 decimal places, so the answer has 3 decimal places: 0.048