To determine the least number of 750 MB capacity CD-ROM discs needed to transfer a 10 GB file, we need to follow a series of steps to convert the units and perform the necessary calculations.
Step 1: Convert GB to MB
First, we need to convert the size of the file from gigabytes (GB) to megabytes (MB) because the capacity of the CD-ROM is given in MB.
1 GB is equal to 1024 MB. Therefore, to convert 10 GB to MB:
[
10 \text{ GB} = 10 \times 1024 \text{ MB} = 10240 \text{ MB}
]
Step 2: Calculate the Number of Discs Required
Next, we need to find out how many 750 MB discs are required to hold 10240 MB. We can do this by dividing the total file size in MB by the capacity of one CD-ROM in MB.
[
\text{Number of discs} = \frac{\text{Total file size in MB}}{\text{Capacity of one disc in MB}} = \frac{10240 \text{ MB}}{750 \text{ MB}}
]
Calculating this gives:
[
\text{Number of discs} = \frac{10240}{750} \approx 13.6533
]
Step 3: Round Up to the Nearest Whole Number
Since we cannot use a fraction of a disc, we need to round up to the nearest whole number. This means we need 14 discs because 13.6533 rounds up to 14.
Conclusion
Thus, the least number of 750 MB capacity CD-ROM discs needed to transfer a 10 GB file is
14.
Explanation of Options
-
A. 75: This option is incorrect because it significantly overestimates the number of discs needed. If we were to use 75 discs, we would have a total capacity of 75 * 750 MB = 56250 MB, which is far more than necessary.
-
B. 31: This option is also incorrect. Using 31 discs would provide a total capacity of 31 * 750 MB = 23250 MB, which again is more than needed but still not the least number of discs.
-
C. 14: This option is correct. As calculated, we need 14 discs to hold the 10 GB file.
-
D. 13: This option is incorrect because, as we calculated, 13 discs would not be sufficient to hold the entire 10 GB file. 13 discs would only provide a total capacity of 13 * 750 MB = 9750 MB, which is less than 10240 MB.
Revision Summary
- Convert file size from GB to MB (1 GB = 1024 MB).
- Calculate the number of discs needed by dividing total file size by disc capacity.
- Always round up to the nearest whole number when dealing with physical items like discs.
- The correct answer is 14 discs, as 13 discs are insufficient to hold the entire file.