# Lesson 5

Decimal Points in Products

### Lesson Narrative

In earlier grades, students have multiplied base-ten numbers up to hundredths (either by multiplying two decimals to tenths or by multiplying a whole number and a decimal to hundredths). Here, students use what they know about fractions and place value to calculate products of decimals beyond the hundredths. They express each decimal as a product of a whole number and a fraction, and then they use the commutative and associative properties to compute the product. For example, they see that $$(0.6) \boldcdot (0.5)$$ can be viewed as $$6 \boldcdot (0.1) \boldcdot 5 \boldcdot (0.1)$$ and thus as $$\left(6 \boldcdot \frac{1}{10}\right) \boldcdot \left(5 \boldsymbol \boldcdot \frac {1}{10}\right)$$. Multiplying the whole numbers and the fractions gives them $$30 \boldsymbol \boldcdot \frac{1}{100}$$ and then 0.3.

Through repeated reasoning, students see how the number of decimal places in the factors can help them place the decimal point in the product (MP8).

### Learning Goals

Teacher Facing

• Generalize (orally and in writing) that the number of decimal places in a product is related to the number of decimal places in the factors.
• Justify (orally) the product of two decimals, which each have only one non-zero digit, by multiplying equivalent fractions that have a power of ten in the denominator.

### Student Facing

Let’s look at products that are decimals.

### Student Facing

• I can use place value and fractions to reason about multiplication of decimals.

Building On