The difference between the greatest 7-digit number and the smallest 5-digit number is 9,989,999.
Understanding the concept of place value is crucial for identifying the greatest and smallest numbers within a given number of digits. These types of calculations are fundamental in mathematics and help build a strong foundation for more complex arithmetic.
Identifying the Numbers
To find the difference, we first need to identify the specific values for the "greatest 7-digit number" and the "smallest 5-digit number."
- Greatest N-Digit Number: This is formed by placing the digit 9 in every position. For a 7-digit number, this means seven 9s.
- The greatest 7-digit number is 9,999,999.
- Smallest N-Digit Number: This is formed by placing the digit 1 in the highest place value position and 0s in all subsequent positions. For a 5-digit number, this means 1 followed by four 0s.
- The smallest 5-digit number is 10,000.
Let's visualize these numbers:
| Description | Number |
|---|---|
| Greatest 7-Digit Number | 9,999,999 |
| Smallest 5-Digit Number | 10,000 |
Calculating the Difference
Once both numbers are identified, the next step is to perform the subtraction. The difference is found by subtracting the smaller number from the larger number.
Calculation:
Greatest 7-Digit Number – Smallest 5-Digit Number
9,999,999 – 10,000 = 9,989,999
This calculation shows that the difference is indeed 9,989,999, as indicated by various mathematical resources.
Practical Insights and Applications
Understanding how to identify and manipulate numbers based on their digit count is a core concept in elementary mathematics. It helps in:
- Understanding Place Value: Reinforces the importance of each digit's position.
- Estimation: Quickly estimating large differences or sums.
- Problem-Solving: Applying these principles to various word problems and real-world scenarios, such as calculating large financial differences or population changes.
For further exploration of number systems and place value, you can refer to educational resources like Khan Academy's Place Value lessons (Note: Link provided as an example of a credible source for number theory).
This straightforward arithmetic operation highlights the vast range between numbers with different digit counts, even when considering the "greatest" and "smallest" within their respective categories.
