A computer does a calculation in 5 nanoseconds. How many of these calculations can the computer do in 1 second?

To find out how many calculations the computer can do in 1 second, we need to convert the time taken for one calculation (5 nanoseconds) to seconds, and then divide 1 second by that time.

[ 1 \text{ second} = 10^9 \text{ nanoseconds} ]

So, to convert 5 nanoseconds to seconds, we divide by ( 10^9 ):

[ 5 \text{ nanoseconds} = \frac{5}{10^9} \text{ seconds} ]

Now, to find out how many calculations can be done in 1 second, we divide 1 second by the time taken for one calculation:

[ \text{Calculations in 1 second} = \frac{1 \text{ second}}{\frac{5}{10^9} \text{ seconds}} ]

[ = \frac{10^9}{5} \text{ calculations} ]

[ = 200,000,000 \text{ calculations} ]

So, the computer can do 200,000,000 calculations in 1 second.

The computer can do ( \frac{1}{5 \times 10^{-9}} ) calculations in 1 second, which is equal to ( 200,000,000 ) calculations.