Pen Drive for Scanned Answer Scripts
Your school plans to scan 240 answer scripts for its own records. Each script averages 12 pages. Every page is scanned at 300 dpi in 24-bit colour; a page is 8.27 in × 11.69 in, giving about 8.7 million pixels per page. The vendor quotes only raw, uncompressed size, and says JPEG compression may reduce it to about one-eighth. The school has a 16 GB pen drive whose usable capacity is about 14.9 GiB, and a 4.7 GB single-layer DVD. The scanner software reports sizes using 1 MB = 1,000,000 bytes and 1 GB = 1,000,000,000 bytes. The head teacher wants a decision: is the pen drive enough for the raw scans, is the DVD enough, and how should the size be reported so that nobody confuses decimal GB with binary GiB? The office also needs a short label for the archive folder stating the raw size in GB and GiB.
1. Estimate the raw storage for all 2,880 pages. Show the per-page calculation, then give the total in decimal MB and GB. Decide whether the 16 GB pen drive and the 4.7 GB DVD are sufficient for raw scans.
Read the worked answer
Per page: 8.7 × 10^6 pixels × 24 bits = 208.8 × 10^6 bits. Divide by 8 to get bytes: 26.1 × 10^6 bytes = 26.1 MB (decimal).
Total pages: 240 scripts × 12 pages = 2,880 pages. Total raw size: 2,880 × 26.1 MB = 75,168 MB = 75.168 GB (decimal).
Decision: the 16 GB pen drive is far too small for raw scans, and the 4.7 GB DVD is also too small. Even the compressed estimate, about 75.168 ÷ 8 = 9.4 GB, exceeds one DVD; it fits the 16 GB pen drive only if the compression claim is reliable and there is room for file-system overhead.
2. Convert 75,168 MB to GiB and explain why a 16 GB pen drive shows about 14.9 GiB. Which unit should the archive label use, and how can the school avoid the confusion?
Read the worked answer
75,168 MB = 75.168 × 10^9 bytes. One GiB = 2^30 = 1,073,741,824 bytes, so 75.168 × 10^9 ÷ 1.073741824 × 10^9 ≈ 70.0 GiB.
The pen drive is sold as 16 GB = 16 × 10^9 bytes. In binary units that is 16 × 10^9 ÷ 2^30 ≈ 14.9 GiB. The missing capacity is not lost; the two numbers use different definitions of “giga”.
The archive label should state both, for example “Raw size: 75.2 GB (70.0 GiB)”. The school should also state the scanner settings and whether compression was applied, so a later reader does not compare a decimal GB figure with a binary GiB figure and conclude that data is missing.
3. The vendor offers to split the archive across three 4.7 GB DVDs if the scans are compressed to one-eighth. Check whether three DVDs are enough, showing your reasoning.
Read the worked answer
Compressed size ≈ 75.168 GB ÷ 8 = 9.396 GB. Three single-layer DVDs provide 3 × 4.7 GB = 14.1 GB of nominal capacity, so 9.396 GB is within the nominal total.
However, the decision should not stop at 9.396 < 14.1. DVD file systems and session overhead reduce usable capacity, and the one-eighth compression figure is only an estimate. A safer plan is to test-compress a sample of pages, measure the actual size, and keep each DVD below its practical limit rather than filling it exactly. Three DVDs are probably enough, but the school should verify after compression and label each disc with its contents.