Rationale
Number n is multiplied by 10.
When the decimal point in a number is moved two places to the left, it is effectively multiplied by 10 twice, resulting in a factor of 100. Similarly, moving the decimal point one place to the right multiplies the number by 10. Therefore, the sum of these two operations, p + s, corresponds to multiplying n by 100 + 10 = 110.
A) 1.01
This choice represents a number slightly above 1, which does not align with the multiplication factor of 110 obtained by adding p and s to n. The value of 1.01 does not reflect the correct relationship between n, p, s, and their sum.
B) 10.001
The number 10.001 is notably higher than the expected result of multiplying n by 110. This value does not correspond to the sum of the two transformations applied to n and is not consistent with the arithmetic operation required to find p + s.
C) 10.01
Since p represents 100n and s represents 10n, adding these values together results in 110n, making the correct choice C, 10.01, the most suitable answer. This number reflects the operation of moving the decimal points in n as described in the question and sums them accurately.
D) 10.1
The value of 10.1 does not match the expected sum of 110n, which arises from moving the decimal point in n as specified in the question. This choice does not align with the multiplication factor associated with the transformations of n to obtain p and s.
Conclusion
In this scenario, the correct answer is option C, 10.01. By understanding how moving the decimal point in a number affects its value, we can deduce that p + s equals 110 × n. The sum of these two transformations results in a factor that multiplies the original number n to produce the final value of 10.01.
