Multiply by Powers of 10
Multiply by Powers of 10 is a Grade 5 math skill in Eureka Math, Chapter 7: Mental Strategies for Multi-Digit Whole Number Multiplication, where students learn that multiplying by 10, 100, or 1,000 shifts digits one, two, or three places to the left on the place value chart. Mastering this skill enables faster mental math and builds a foundation for scientific notation and decimal operations.
Key Concepts
Property Multiplying a whole number by a power of 10 ($10, 100, 1000, \dots$) involves annexing (adding) zeros to the end of the number. The number of zeros added is equal to the number of zeros in the power of 10. $n \times 10 = n0$ $n \times 100 = n00$ $n \times 1000 = n000$.
Examples $5 \times 10 = 50$ $82 \times 100 = 8200$ $45 \times 1000 = 45000$.
Explanation When you multiply a whole number by 10, 100, or 1000, you are making the number that many times larger. This has the effect of shifting each digit to a larger place value. A simple way to find the product is to count the number of zeros in the power of 10 and add that many zeros to the end of the original number.
Common Questions
What happens to digits when you multiply by powers of 10?
Each digit shifts one place to the left for each power of 10 you multiply by. Multiplying by 10 shifts one place, by 100 shifts two places, and by 1,000 shifts three places.
How do you multiply large numbers by 100 mentally?
Shift all the digits two places to the left on the place value chart, which is the same as adding two zeros to the end of a whole number.
Why is learning to multiply by powers of 10 important in Grade 5?
This skill underpins decimal multiplication, scientific notation, and metric unit conversions, making it essential for advanced 5th grade math and middle school content.
What is Chapter 7 of Eureka Math Grade 5 about?
Chapter 7 focuses on Mental Strategies for Multi-Digit Whole Number Multiplication, including multiplying by multiples and powers of 10.