Writing Numbers in Expanded Form
This Grade 4 Eureka Math skill teaches students to write multi-digit numbers in expanded form by expressing each digit as the product of that digit and its place value. For example, 473 = 400 + 70 + 3, and 2,158 = 2,000 + 100 + 50 + 8. Students learn to recognize that each digit contributes its face value times its place value unit. This place value decomposition skill, from Chapter 11 of Eureka Math Grade 4, supports multi-digit multiplication by making the distributive property visible and concrete.
Key Concepts
A multi digit number can be written in expanded form by expressing it as the sum of the values of its digits. For example, a four digit number can be written as: $$Thousands + Hundreds + Tens + Ones$$.
Common Questions
What is expanded form?
Expanded form writes a number as the sum of the values of each digit by place value. For 473: 400 + 70 + 3.
How do you write 2,158 in expanded form?
2,158 = 2,000 + 100 + 50 + 8. Each digit is multiplied by its place value: 2 thousands + 1 hundred + 5 tens + 8 ones.
How do you handle zeros in expanded form?
Skip the place values with a 0 digit. For 6,092: 6,000 + 90 + 2. The hundreds place is 0, so it is omitted.
How does expanded form connect to multiplication?
In expanded form, each part (like 2,000 or 50) is a single digit times a power of 10. This directly shows the distributive property used in the partial products multiplication algorithm.
What is the expanded form of 6,092?
6,092 = 6,000 + 90 + 2. There is no hundreds digit to include.