Represent
Representing a number in expanded form shows the value of each digit as a sum: 813 = 800 + 10 + 3, and 407 = 400 + 7 (the zero tens place is omitted or written as 0). Students also express numbers in standard form (813) and word form (eight hundred thirteen). This skill is central to Saxon Math Intermediate 4 and builds deep place value understanding in 4th grade math — knowing that 813 is truly 800 + 10 + 3 makes addition, subtraction, and multiplication algorithms make intuitive sense.
Key Concepts
Property Expanded form is a way of writing a number to show the value of each digit. It is shown as a sum of each digit multiplied by its matching place value. For example, 813 is written as $800+10+3$.
Examples Number 813 is written as $800 + 10 + 3$ and in words as 'eight hundred thirteen.' Number 407 is written as $400 + 7$ and in words as 'four hundred seven.' Adding in dollars, $189 \text{ dollars} + 298 \text{ dollars}$, can be seen as $(100+200)+(80+90)+(9+8)$.
Explanation Think of expanded form as showing a number's secret recipe! The number 813 isn't just a random sequence; it's a combination of 8 hundreds, 1 ten, and 3 ones all mixed together. Expanded form breaks the number down into its core ingredients, showing you what each digit is truly worth based on its place value in the final number.
Common Questions
What is expanded form in math?
Expanded form writes a number as the sum of the values of each digit. For example, 813 in expanded form is 800 + 10 + 3. Each addend shows the place value contribution of one digit.
How do you write a number in expanded form?
Multiply each digit by its place value. For 4,256: 4×1000 + 2×100 + 5×10 + 6×1 = 4,000 + 200 + 50 + 6. Write these as a sum.
How do you write a number that has a zero in expanded form?
Skip the zero place value or write it as 0. For 407: 400 + 0 + 7, which is often simplified to 400 + 7. The zero shows no tens, but the other places are unchanged.
What are the three ways to represent a number?
Standard form (813), expanded form (800 + 10 + 3), and word form (eight hundred thirteen). Being fluent in all three shows true understanding of what a number means.
When do students learn expanded form?
Expanded form is introduced in early elementary grades and extended in 4th grade. Saxon Math Intermediate 4 uses expanded form to deepen place value understanding and connect it to addition and multiplication algorithms.
How does expanded form help with multi-digit multiplication?
Expanded form underpins the partial products method. To multiply 32 × 4, expand 32 as 30 + 2: (30 × 4) + (2 × 4) = 120 + 8 = 128. Seeing numbers in expanded form makes the distributive property visible.