Definition
Standard form and expanded form are two ways to represent numbers, helping us to understand the value of each digit.
- Standard form is the typical way we write numbers, like 64,076,750.
- Expanded form breaks down the number to show the value of each digit based on its place value, using addition. For example, 64,076,750 in expanded form is 60,000,000 + 4,000,000 + 70,000 + 6,000 + 700 + 50.
Description
When converting between standard and expanded form, we use the powers of ten to understand the place value of each digit in the number.
- Expanded to Standard Form:
- When given a number in expanded form, we add up each place value to write it in standard form.
- Example: If we see 4,000,000 + 700,000 + 70,000 + 4,000 + 900 + 60, we add these values together to get the standard form 4,774,960.
- Standard to Expanded Form:
- When converting a number from standard form to expanded form, we break down the number based on each digit’s place value.
- Example: The number 84,054,169 in expanded form is 80,000,000 + 4,000,000 + 50,000 + 4,000 + 100 + 60 + 9.
Why This is Important
Understanding how to convert between standard and expanded form is essential for grasping place value and the powers of ten. This skill helps in understanding how each digit contributes to the overall value of the number, building a strong foundation for more advanced math concepts like decimals and scientific notation.
Let's Practice!
Use the steps above to convert the following numbers between standard and expanded form, reinforcing your understanding of place value and the powers of ten.
