Placing the Decimal Point in a Product
Placing the Decimal Point in a Product is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) where students learn to multiply decimals by first multiplying as whole numbers, then counting the total decimal places in both factors and placing the decimal point in the product accordingly. This rule generalizes decimal multiplication beyond whole number factors.
Key Concepts
Property To multiply decimals, first multiply the numbers as if they were whole numbers. The total number of decimal places in the product is the sum of the number of decimal places in the factors being multiplied.
Examples To solve $0.3 \times 0.07$: First, find the product of the whole numbers, $3 \times 7 = 21$. The factors have one and two decimal places, respectively, for a total of three ($1+2=3$). So, the product is $0.021$. To solve $1.2 \times 0.5$: First, find the product of the whole numbers, $12 \times 5 = 60$. Each factor has one decimal place, for a total of two ($1+1=2$). So, the product is $0.60$ or $0.6$.
Explanation This rule works because multiplying by decimals is like multiplying by fractions with denominators of 10, 100, etc. When you multiply the numbers, you are also multiplying their place values. Counting the decimal places is a shortcut for determining the correct place value of the final product. This method allows you to use whole number multiplication skills and then correctly place the decimal point.
Common Questions
How do you place the decimal point in a multiplication product?
Multiply the numbers as whole numbers. Count the total decimal places in both factors. Place the decimal point in the product so it has that total number of decimal places. For example, 0.3 × 0.07: 3 × 7 = 21, total decimal places = 1 + 2 = 3, so product = 0.021.
What is the rule for decimal places in a multiplication product?
The number of decimal places in the product equals the sum of decimal places in both factors. For 1.2 × 0.5: each has 1 decimal place, so product has 2 decimal places: 12 × 5 = 60, product = 0.60 = 0.6.
What chapter covers placing the decimal point in a product in Illustrative Mathematics Grade 5?
Placing the decimal point in a product is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.
Why does the total decimal places rule work for multiplication?
Multiplying decimals is equivalent to multiplying fractions with powers of 10 in the denominator. When you multiply the denominators (powers of 10), you get a higher power of 10, which corresponds to more decimal places in the result.
What is an example of placing a decimal point in a product?
0.3 × 0.07: multiply 3 × 7 = 21. Factor 1 has 1 decimal place, factor 2 has 2 decimal places, total = 3. Place decimal 3 places from the right: 0.021.