Base-Ten System Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
mediumWrite 3,407 in expanded form using powers of 10.
Solution
- 1 Identify each digit's place value: 3 is in the thousands place (), 4 is in the hundreds place (), 0 is in the tens place (), 7 is in the ones place ().
- 2 Write each digit multiplied by its place value: .
- 3 Simplify: โ.
Answer
Expanded form reveals how our number system works: each digit's value depends on its position. The digit 0 in the tens place is a placeholder โ it contributes nothing to the value but is essential for keeping other digits in the correct positions.
About Base-Ten System
The positional numeral system using ten as its base, where each digit's value depends on its position, with each place worth ten times the place to its right.
Learn more about Base-Ten System โMore Base-Ten System Examples
Example 1 easy
Express [formula] as a sum of powers of 10.
Example 2 mediumWhy does multiplying any whole number by 10 append a zero? Explain using the base-ten structure.
Example 4 easyWhat is the value of [formula], [formula], [formula], and [formula]?
Example 5 mediumA number [formula]. What is [formula]?