Multiplying Decimals by Whole Numbers Using Place Value
To multiply a decimal by a whole number, treat the decimal as a whole number of its smallest place value unit (tenths, hundredths, or thousandths), multiply, then express the product in that same unit. For example, 6 times 0.8 becomes 6 times 8 tenths equals 48 tenths equals 4.8. This Grade 5 math skill from Eureka Math Chapter 5 covers multiplying decimals using place value understanding.
Key Concepts
When multiplying a whole number by a decimal, you can treat the decimal as a whole number of its smallest place value unit (e.g., tenths, hundredths, or thousandths). Multiply the whole numbers, and then express the product using that same place value unit. For example, $3 \times 0.4$ is the same as $3 \times 4 \text{ tenths}$, which equals $12 \text{ tenths}$ or $1.2$.
Common Questions
How do you multiply a decimal by a whole number using place value?
Rename the decimal as a whole number of its smallest unit (like tenths or hundredths), multiply the whole numbers, then express the product using that same unit. For example, 6 times 0.8 is 6 times 8 tenths equals 48 tenths equals 4.8.
What does it mean to think of 0.35 as hundredths?
Thinking of 0.35 as 35 hundredths means treating 35 as the number of hundredth-sized pieces, allowing you to multiply by a whole number using familiar whole number multiplication, then convert back.
Why does this place value method work for decimal multiplication?
This method works because it transforms an unfamiliar decimal multiplication into a familiar whole number multiplication, with the place value unit tracking where the decimal point goes in the final answer.
What is an example of multiplying 4 times 3.25?
Think of 3.25 as 325 hundredths. Multiply 4 times 325 equals 1300 hundredths. Convert 1300 hundredths back to a decimal: 13.00, or simply 13.