Comparing Digit Values Using Expanded Form
Comparing digit values using expanded form is a Grade 5 math skill in enVision Mathematics, Chapter 1: Understand Place Value. Expanded form breaks a number into the sum of each digit multiplied by its place value, making it easy to see that the same digit holds 10 times more value when it moves one position to the left. This skill supports understanding of relative place value and number comparisons.
Key Concepts
Property Expanded form breaks a number into a sum of its place values. This makes it easier to compare the value of the same digit in different positions.
Examples In the number 34,381, what is the relationship between the value of the 3 in the ten thousands place and the 3 in the hundreds place? Expanded Form: $3 \times 10,000 + 4 \times 1,000 + 3 \times 100 + 8 \times 10 + 1 \times 1$. The value of the first 3 is $30,000$ and the value of the second 3 is $300$. Since $30,000 = 300 \times 100$, the first 3 is 100 times the value of the second 3. Compare the values of the digit 9 in the number 992,450. Expanded Form: $900,000 + 90,000 + 2,000 + 400 + 50$. The value of the 9 in the hundred thousands place is $900,000$. The value of the 9 in the ten thousands place is $90,000$. The value of the first 9 is 10 times the value of the second 9.
Explanation Writing a number in expanded form separates each digit into its individual place value. This allows you to directly see and compare the value of each digit. By looking at the terms in the expanded form, you can determine how many times greater one digit''s value is than another''s. This method reinforces the idea that a digit''s position determines its value.
Common Questions
What is expanded form and how does it help compare digit values?
Expanded form writes a number as a sum of each digit times its place value (e.g., 3,452 = 3,000 + 400 + 50 + 2). It makes it easy to see how much each digit contributes to the total.
How do you compare the same digit in different places?
A digit is 10 times greater in value when it moves one place to the left. For example, the 3 in 300 is 10 times the value of the 3 in 30.
How do you write 4,507 in expanded form?
4,507 = 4,000 + 500 + 0 + 7 = 4×1,000 + 5×100 + 0×10 + 7×1.
Where is expanded form and digit comparison taught in enVision Grade 5?
Chapter 1: Understand Place Value in enVision Mathematics, Grade 5.
Why is expanded form important in 5th grade math?
It helps students understand the relationship between digits and their values, which supports operations with large numbers, rounding, and comparisons.