9. In the number shown, how many × larger is the place value of the underlined 5 compared with the place value of the 5 with no underline?
Answer: C
The place value of the underlined 5 is 10,000 times larger than the place value of the other 5.
The underlined 5 in the number 345.792 is in the thousands place, representing 5,000, while the other 5 is in the tenths place, representing 0.5. Therefore, the underlined 5 is 10,000 times larger than the other 5.
A) 1000
Option A is incorrect because the underlined 5 represents 5,000, while the other 5 is 0.5. The ratio of 5,000 to 0.5 is not 1,000; it is 10,000.
B) 5000
Option B is also incorrect. Although the underlined 5 represents 5,000, comparing it to the other 5, which is 0.5, gives a much larger ratio than 5,000.
C) 10000
This option is correct as the place value of the underlined 5 (5,000) is indeed 10,000 times larger than the place value of the other 5 (0.5). The calculation is straightforward: 5,000 divided by 0.5 equals 10,000.
D) 50000
Option D is incorrect. The comparison does not yield a value of 50,000, as the ratio between the two place values is 10,000, not 50,000.
Conclusion
The correct answer, C, demonstrates that the place value of the underlined 5 is 10,000 times larger than that of the other 5. All other options fail to accurately represent the ratio between the two place values, confirming that C is the only viable choice.