Multiply by Powers of 10
Multiply by Powers of 10 is a Grade 5 math skill from Eureka Math, Chapter 7: Mental Strategies for Multi-Digit Whole Number Multiplication. Students learn that multiplying a whole number by 10, 100, or 1,000 means annexing (adding) zeros equal to the power of 10. This mental math strategy builds place value understanding for multi-digit multiplication.
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
How do you multiply a whole number by powers of 10?
Annexing zeros to the end of the number: multiplying by 10 adds one zero, by 100 adds two zeros, by 1,000 adds three zeros.
What does it mean to annex zeros when multiplying by 10?
Annexing zeros means adding zeros to the right of a number. When you multiply 45 by 100, you annex two zeros to get 4,500.
Why does multiplying by powers of 10 add zeros?
Each multiplication by 10 shifts all digits one place value to the left, which is equivalent to adding a zero at the end for whole numbers.
What is the Eureka Math Grade 5 lesson on multiplying by powers of 10?
Chapter 7 of Eureka Math Grade 5 covers mental strategies for multi-digit multiplication, including multiplying whole numbers by 10, 100, and 1,000 by annexing zeros.
How many zeros do you add when multiplying by 1,000?
You add three zeros when multiplying by 1,000, because 1,000 has three zeros (three powers of 10).