Difficulty: Medium

Average Score: 57%

Train 4 traveled 1,603 miles from Seattle, Washington, to Tucson, Arizona, in 37 hours. Train B traveled 1,090 miles from Portland, Oregon, to San Diego, California, in 24 hours.

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?

Rationale

In the number shown, the place value of the underlined 5 is 10,000 times larger compared to the place value of the 5 with no underline.

In this scenario, the underlined 5 represents a value in the ten-thousands place, while the unmarked 5 is in the thousands place. Since the place values differ by a factor of ten for each position, the underlined 5 is ten times larger than the thousands place for every shift left.

A (1,000) YOUR ANSWER

The choice of 1,000 suggests that the underlined 5 is only one thousand times larger than the unmarked 5. However, since the underlined 5 is in the ten-thousands place and the other 5 is in the thousands place, the actual difference is a factor of ten, leading to the conclusion that the underlined value is much larger.

B (5,000) YOUR ANSWER

Selecting 5,000 implies that the underlined 5 is five thousand times larger than the unmarked 5. This is incorrect because the place values do not align to produce this ratio; rather, they differ by a factor of ten, making 5,000 an underestimate of the actual comparison.

C (10,000) CORRECT

This choice correctly identifies that the underlined 5, located in the ten-thousands place, is ten times larger than the thousands place value of the unmarked 5. Therefore, it is indeed 10,000 times larger than the 5 without the underline, making it the accurate answer.

D (50,000) YOUR ANSWER

Choosing 50,000 suggests an incorrect multiplication factor of five times ten-thousands over thousands. This choice overestimates the relationship between the two 5s, as they only differ by a factor of ten, not five, leading to a misunderstanding of their respective place values.

Conclusion

In comparing the place values of the underlined and unmarked 5s, the correct answer shows that the underlined 5, which is in the ten-thousands place, is 10,000 times larger than the 5 in the thousands place. This distinction highlights the importance of understanding place value in numerical comparisons and confirms that the only correct ratio is represented by choice C.

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?

In the number shown, the place value of the underlined 5 is 10,000 times larger compared to the place value of the 5 with no underline.

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