Generalizing the Pattern: Shifting Digits by Powers of 10
When multiplying or dividing by a power of 10 (10, 100, 1000), each digit shifts left or right on the place value chart by the number of zeros in the power of 10. Multiplication shifts digits left (increasing value) and division shifts digits right (decreasing value). This Grade 5 math skill from Eureka Math Chapter 1 covers multiplicative patterns on the place value chart.
Key Concepts
When multiplying or dividing by a power of 10, 100 and 1,000, the number of zeros in the power of 10 indicates how many places each digit shifts on the place value chart. Multiplication shifts digits to the left (increasing value), and division shifts digits to the right (decreasing value).
Common Questions
How do digits shift when multiplying by powers of 10?
When multiplying by 10, 100, or 1000, each digit shifts left by the number of zeros in the power of 10. For example, multiplying by 100 shifts each digit two places to the left.
How do digits shift when dividing by powers of 10?
When dividing by 10, 100, or 1000, each digit shifts right by the number of zeros in the power of 10. For example, dividing by 1000 shifts each digit three places to the right.
Why do digits shift when multiplying by powers of 10?
Each place on the value chart represents a value 10 times greater than the place to its right, so multiplying by 10 is equivalent to moving each digit one position to a higher place value.
How does the place value chart help with powers of 10?
A place value chart visually shows how digits move left or right when multiplied or divided by powers of 10, making it easier to understand the relationship between place values.