Definition:
Finding missing numbers in expanded form involves identifying the missing place value that completes the given number. To see the missing number, examine each place value to understand what is missing.
Example 1:
Find the missing number in the expanded form:
3000+500+___+3=3,583.
Solution:
- Break down the standard number, 3,583, by place values:
- Thousands: 3000
- Hundreds: 500
- Tens: 80
- Ones: 3
- Compare the expanded form with the given components to find the missing value.
Final solution: The missing number is 80, so 3000+500+80+3=3,583.
Example 2:
Problem: Find the missing number in the expanded form:
40000+___+300+20+7=45,327.
Solution:
- Break down the standard number, 45,327, by place values:
- Ten thousand: 40000
- Thousands: 5000
- Hundreds: 300
- Tens: 20
- Ones: 7
- The missing place value is the thousands.
Final solution: The missing number is 5000, so 40000+5000+300+20+7=45,327.
Example 3:
Problem: Find the missing number in the expanded form:
___+2000+600+50+9=12,659.
Solution:
- Break down the standard number, 12,659, by place values:
- Ten thousand: 10000
- Thousands: 2000
- Hundreds: 600
- Tens: 50
- Ones: 9
- The missing place value is 10,000.
Final solution: The missing number is 10000, so 10000+2000+600+50+9=12,659.
Example 4:
Problem: Find the missing number in the expanded form:
80000+9000+___+70+2=89,372.
Solution:
- Break down the standard number, 89,372, by place values:
- Ten thousand: 80000
- Thousands: 9000
- Hundreds: 300
- Tens: 70
- Ones: 2
- The missing place value is the hundreds.
Final solution: The missing number is 300, so 80000+9000+300+70+2=89,372.
Why it matters:
Converting expanded numbers to standard form helps students understand place value and the composition of numbers. It strengthens their ability to read, write, and work with large numbers in real-life contexts. This skill is fundamental for performing accurate calculations and solving advanced math problems.
By practicing expended numbers, you can solve real-world problems quickly!
Let’s practice and evaluate your work together by expended numbers.
