Our final answer must represent "number of mosquitos." This verifies that the correct calculation would be
1000 mosquitos 10.5 hours
----------------------- x --------------------
1 hour 1
Multiply this out. Note that "hours" will cancel.
Whats your result?
Supposing that your result looked like xxxxx times 10^0,
you'd convert this into scientific notation by moving the decimal place four units to the left (obtaining x.xxx) and then increasing the exponent of 10 from zero to four (obtaining 10^4).
Then your answer would have the form x.xxx times 10^4 (mosquitos)