In this lesson, students use what they know about fractions and place value to reason about products of decimals beyond the hundredths. They first recall that the fractions , , and are equivalent to the decimals 0.1, 0.01, and 0.001, respectively, and that multiplying a number by these values is equivalent to dividing the number by 10, 100, and 1,000. Students observe how such operations affect the number of decimal places in the resulting products or quotients.

Next, students express each decimal factor as a product of a whole number and a fraction, and then use the commutative and associative properties to compute the product. For example, they see that can be viewed as and thus as . Multiplying the whole numbers and the fractions gives , which is 0.3.

As they reason about the relationship between decimals and fractions, and about its effects on the number of decimal places in the product, students practice making use of the structure of the base-ten system (MP7).