Applying Digit Shift Patterns for 10, 100, 1000
Applying digit shift patterns means using the rule that multiplying by 10 shifts digits one place left, by 100 shifts two places left, and by 1000 shifts three places left, and reversing these shifts for division. This visual shortcut replaces the need to draw a full place value chart for every calculation. This Grade 5 math skill from Eureka Math Chapter 1 reinforces multiplicative patterns on the place value chart.
Key Concepts
When multiplying by a power of 10, every digit shifts to the left. The number of places shifted is equal to the number of zeros in the power of 10.
When dividing by a power of 10, every digit shifts to the right. The number of places shifted is equal to the number of zeros in the power of 10.
Common Questions
What is the digit shift pattern for multiplying by 100?
Multiplying a number by 100 shifts every digit two places to the left on the place value chart, since there are two zeros in 100.
What is the digit shift pattern for dividing by 1000?
Dividing a number by 1000 shifts every digit three places to the right on the place value chart, since there are three zeros in 1000.
How is the digit shift pattern a mental math shortcut?
Instead of drawing a place value chart each time, you can quickly shift digits left or right by counting the zeros in the power of 10, making it faster to multiply and divide mentally.
What is an example of digit shifting with decimals?
For 3.45 times 100, shift each digit two places left: 3 moves from ones to hundreds, 4 moves from tenths to tens, and 5 moves from hundredths to ones, giving 345.