Question

Factor label calculations (Dimensional Analysis) : A student (ZA) shopping for computer

memory saw a sale for

50GB at 10$ , or 200MB for 7$ or 10TB for 20$

Which one has the least cost per megabyte? Show calculations in each case.

Answer 1

Here to find out the least cost we have to convert all of the memory units into a same unit and the smallest possible unit is MB.

Useful Conversions

1024 MB = 1 GB. 1024 GB = 1 TB

So for first case 50 GB is equal to 50*1024= 51200 MB at 10 $ So at 1 $ you get 5120 MB

For 2nd case 200 MB for 7 $ . So at 1 $ you get 200/7= 28.57 MB.

For 3rd case 10 TB= 10*1024 = 10240 GB = 10240*1024 = 10485760 MB at 20 $. So at 1 $ you get 10485760 / 20 = 524288 MB.

So the least cost per metabyte will be the last one , as per same cost in every cases we are getting highest amount of MB.

1st case cost per MB = 1 / 5120 = 1.953 *10^-4 $

2nd case cost per MB = 1 / 28.57 = 35 *10^-3 $

3rd case cost per MB = 1 / 524288 = 1.907 *10^-6 $