13. The number p is obtained by moving the decimal point 2 places to the left in the positive number n. The number s is obtained by moving the decimal point 1 place to the right in the number n. The number p + s how many × n?
Answer: C
p + s is equal to 10.01 times n.
When the decimal point in the positive number n is moved 2 places to the left, it results in the number p, which can be expressed as p = n / 100. Moving the decimal point 1 place to the right results in the number s, or s = n × 10. Therefore, p + s = (n / 100) + (n × 10) = (n / 100) + (1000n / 100) = 10.01n.
A) 1.01
This option is incorrect because it suggests that the sum of p and s is only a small fraction of n. Given the calculations, p should be a very small number compared to s, making 1.01 an implausible total for p + s when compared to n.
B) 10.001
This option is also incorrect as it is slightly higher than the calculated total of 10.01n. The calculations show that while p contributes minimally to the total, it does not account for an extra 0.001 in addition to the correct value.
C) 10.01
This option is correct because it accurately represents the sum of p and s in relation to n. The derived equation shows that moving the decimal points as described results in p + s equaling 10.01n, aligning perfectly with this choice.
D) 10.1
This option is incorrect as it exceeds the calculated value of 10.01. Though it is close, it misrepresents the precise relationship established in the problem where p contributes a very small amount to the total.
Conclusion
The correct answer, 10.01, reflects the accurate relationship between the numbers p and s in relation to n. All other options fail to align with the mathematical derivation provided, confirming that the only viable option is C.