Question

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

Answer 1

As we know that $1$ second = ${10^{ - 9}}$ nanoseconds, and we know that one calculation is completed in $5$ nanoseconds, therefore we simply just divide $1$ with $5 \times {10^{ - 9}}$ to get our required number of calculations.

Complete step-by-step solution:
In this question, we are asked to find the number of calculations that a computer can perform in $1$ second, given that it can complete a single calculation in $5$ nanoseconds.
Now, we know that $1$ second =${10^{ - 9}}$ nanoseconds
In $5 \times {10^{ - 9}}$ seconds, the computer can complete = $1$ calculation
Therefore, in $1$ second, the computer can complete = $\dfrac{1}{{5 \times {{10}^{ - 9}}}}$ calculations

Number of calculations completed in $1$ second = $2 \times {10^8}$

Note: Such types of questions are known as story sums. In order to solve these sums accurately, one must thoroughly read and understand what the question requires. We form our equation accordingly once we have found what we need to place as our unknown constant and relate it with the other variables in the question. We usually place the known variables on the left hand side and place the unknown variables on the right hand side so it is easier for us to calculate and solve the required sum.
In SI units, time is expressed in the form of seconds. Now in order to express values larger than second, we use units like mega seconds, giga seconds etc. while to express values of time smaller than second, we use prefixes like nano, micro, milli, etc.
We know that
$1s = {10^{ - 6}}\mu s$
$1s = {10^{ - 9}}ns$
Some common conversions of seconds are:
$1$second = $\dfrac{1}{{60}}$ minutes
$1$ second= $\dfrac{1}{{3600}}$ hours