Sure! Let's break down and solve the problem step by step.
### Expanded Form
To write the number 44,910 in expanded form, we need to express it as a sum of its place values. Here’s how we do it:
1. The first digit is 4 in the ten-thousands place, so it represents 40,000.
2. The second digit is 4 in the thousands place, so it represents 4,000.
3. The third digit is 9 in the hundreds place, so it represents 900.
4. The fourth digit is 1 in the tens place, so it represents 10.
5. The fifth digit is 0 in the ones place, so it represents 0.
Hence, 44,910 in expanded form is:
[tex]\[ 40,000 + 4,000 + 900 + 10 + 0 \][/tex]
### Checking Digit Values
Next, we need to determine if any digits in the number have a value that is 10 times the value of another digit.
- 40,000 has no corresponding digit that is 1/10th of its value.
- 4,000 is 1/10th of 40,000.
- 900 does not have a corresponding digit that is 1/10th of its value within this number.
- 10 does not have a corresponding digit that is 1/10th of its value within this number.
- 0 has no effect since it represents no value.
From the analysis, we can see that 4,000 is 1/10th of 40,000. Thus, there is a pair of digits where one digit’s place value is exactly 10 times another's place value.
### Conclusion
1. The expanded form of 44,910 is:
[tex]\[ 40,000 + 4,000 + 900 + 10 + 0 \][/tex]
2. Yes, there are digits in the number where one digit’s value is 10 times the value of another digit. Specifically, the digit representing 4,000 is 1/10th of the digit representing 40,000.
