A computer can process 100 records of data in 200 milliseconds. If a millisecond is 1/1000 of a second, how many seconds does it take to process a file of 1000 records?

What will be an ideal response?

Solution 1 (using step-by-step reasoning):
• If it takes 200 milliseconds to process 100 records, it will take 10 times longer (2000 milliseconds) to process a file of 1000 records
• 2000 milliseconds is the same as 2 seconds, because it takes 1000 of the little 1/1000 second parts to make one second.
Thus, it takes 2 seconds to process the file.
Notice: The above reasoning used reciprocals of the information provided as input.
• If 100 records are processed in 200 milliseconds,
then it takes 200 milliseconds to process 100 records.
• If a millisecond is 1/1000 second, then one second is 1000 milliseconds.
Thinking in reciprocal terms makes the reasoning easier.

Solution 2 (using unit analysis)
Use unit conversion technique presented later in this chapter.
• One millisecond is 1/1000 second gives two reciprocal conversion factors: 1 / 1000 (seconds / millisecond) 1000 (milliseconds / second)
• 100 records processed in 200 milliseconds gives two reciprocal factors: 100 / 200 (records / millisecond) 200 / 100 (milliseconds / record)
• 1000 records in the file gives two reciprocal factors: 1000 (records / file) 1/1000 (file / record)
• Now, select the appropriate factors to find number of seconds to process the file:
x (seconds / file) = 1 / 1000 (seconds / milliseeertd)
* 200 / 100 (frtilliseeerids / reeefd)
* 1000 (records / file)
x (seconds / file) = (1 / -IOW) * (200 / * -1-000 (seconds / file)
= 2 (seconds / file)
Thus, it takes 2 seconds to process the file.