Place Value Shifts when Multiplying by Powers of 10
Multiplying a number by a power of 10 makes the number larger by increasing the place value of each of its digits. The number of zeros in the multiplier (, , or ) tells you exactly how many places to the left each digit moves on the place value chart. For example, multiplying by moves a digit two places to the left, making its value times greater. This 4th grade skill appears in Chapter 10 of Eureka Math Grade 4 (Multiplication by 10, 100, and 1,000) and lays the groundwork for more advanced mathematical reasoning in 5th grade.
Key Concepts
When multiplying a number by $10$, $100$, or $1,000$, every digit in the number shifts to the left on a place value chart. The number of places shifted corresponds to the number of zeros in the multiplier: one place for $10$, two for $100$, and three for $1,000$.
Common Questions
What is Place Value Shifts when Multiplying by Powers of 10?
Multiplying a number by a power of 10 makes the number larger by increasing the place value of each of its digits. It is covered in Multiplication by 10, 100, and 1,000 in Eureka Math Grade 4.
How do you place value shifts when multiplying by powers of 10?
The number of zeros in the multiplier (, , or ) tells you exactly how many places to the left each digit moves on the place value chart. For example, multiplying by moves a digit two places to the left, making its value times greater. It is important to remember that all digits in the number shift together to maintain their value relative to each other.
Why is place value shifts when multiplying by powers of 10 important in 4th grade math?
Mastering place value shifts when multiplying by powers of 10 builds conceptual understanding of 4th grade math and directly supports skills in grades 5 and 6. Students who understand the reasoning — not just the steps — make fewer errors when this concept appears in new contexts such as algebra, measurement, or advanced fractions.
Which textbook covers Place Value Shifts when Multiplying by Powers of 10?
This skill is taught in Eureka Math, Grade 4, in Chapter 10: Multiplication by 10, 100, and 1,000. Eureka Math is a Common Core-aligned curriculum used in many US elementary schools.
What are common mistakes when learning place value shifts when multiplying by powers of 10?
Common mistakes include confusing the whole and the part, skipping intermediate steps, and not verifying the final answer. For place value shifts when multiplying by powers of 10, students should always re-read the problem after solving to confirm their answer makes sense.
When do students learn place value shifts when multiplying by powers of 10?
Students learn place value shifts when multiplying by powers of 10 in 4th grade. In Eureka Math, it is part of Chapter 10: Multiplication by 10, 100, and 1,000.
Is Place Value Shifts when Multiplying by Powers of 10 a 4th grade Common Core skill?
Yes. Place Value Shifts when Multiplying by Powers of 10 is a 4th grade Common Core math skill. It is part of Multiplication by 10, 100, and 1,000 in Eureka Math, Grade 4 and is typically taught in the second half of the 4th grade school year.