In this lesson, students continue to develop methods for computing products of decimals by reasoning about properties of base-ten numbers, as well as by reasoning about the area of a rectangle.

Previously, students multiplied decimals by first expressing them as fractions with a power of 10 for the denominator. Here, they see that they can also multiply decimals by powers of 10 to get whole numbers, multiply the whole numbers, and then divide the result by the same powers of 10. For example, to multiply , students may compute and to have whole numbers 25 and 16, multiply these to get 400, and then divide 400 by 1,000 to invert the initial multiplication by 1,000.

In an optional activity, students use the area of a rectangle that is decomposed into unit squares to represent and find products of decimals. They see that a rectangle that represents , for instance, can also represent , , or because they all share a common structure. Because each pair of factors is related to  by a power of 10 or a power of , we can multiply 8 by these powers to find the other products.