On a hypothetical relative mass scale, the average mass of the atoms of element A was assigned a value of 64.00 gigs. The average mass of the atoms of element B is 36.40% that of element A, and the average mass of the atoms of element C is 6.43 times the mass of A. What is the average mass of the atoms of element C rounded to the nearest 0.01 gigs?
A) 34.98 gigs
B) 439.70 gigs
C) 87.67 gigs
D) 411.52 gigs
The correct answer and explanation is :
We are given the following information:
- The average mass of the atoms of element A is 64.00 gigs.
- The average mass of the atoms of element B is 36.40% that of element A.
- The average mass of the atoms of element C is 6.43 times the mass of element A.
Step 1: Find the average mass of element B
We are told that the mass of element B is 36.40% of the mass of element A. To calculate the mass of element B, we multiply the mass of element A by 36.40% (or 0.364):
[
\text{Mass of element B} = 64.00 \, \text{gigs} \times 0.364 = 23.296 \, \text{gigs}
]
Thus, the average mass of the atoms of element B is 23.296 gigs.
Step 2: Find the average mass of element C
Next, we know that the mass of element C is 6.43 times the mass of element A. To calculate the mass of element C, we multiply the mass of element A by 6.43:
[
\text{Mass of element C} = 64.00 \, \text{gigs} \times 6.43 = 411.52 \, \text{gigs}
]
Thus, the average mass of the atoms of element C is 411.52 gigs.
Step 3: Round the result
The problem asks for the mass of element C rounded to the nearest 0.01 gigs. Since 411.52 gigs is already rounded to two decimal places, no further rounding is necessary.
Final Answer
The average mass of the atoms of element C is 411.52 gigs, so the correct answer is:
D) 411.52 gigs.
