Question

If a computer can do a calculation in \[0.0000004\] seconds how long in seconds would it take the computer to do \[6,000,000,000,000\] calculations. Write your answer in scientific notations?

Answer 1

Hint: In the given question, we have been asked to find the number of seconds it would take for the computer to do \[6,000,000,000,000\] calculations. Now here we have given that a computer will do a single calculation in \[0.0000004\] seconds so first of all you should convert this term into scientific notation first and then solve the question. And to solve you just have to do the multiplication of both the terms.

Complete step by step solution:
Now we have to find the number of seconds required by the computer to complete \[6,000,000,000,000\] calculations, for this first of all convert both the given terms to scientific notations i.e.
 \[0.0000004 = 4 \times {10^{ - 7}}\]
 \[6,000,000,000,000 = 6 \times {10^{12}}\]
Now multiply both the terms because if computer can do a single calculation in \[4 \times {10^{ - 7}}\] seconds then it will take \[(4 \times {10^{ - 7}}) \times (6 \times {10^{12}})\] seconds to solve \[6 \times {10^{12}}\] calculations.
Now we will find the product of both the terms i.e.
 \[
   \Rightarrow (4 \times {10^{ - 7}}) \times (6 \times {10^{12}}) \\
   \Rightarrow (4 \times 6) \times ({10^{ - 7}} \times {10^{12}}) \\
   \Rightarrow 24 \times {10^{( - 7 + 12)}} \\
   \Rightarrow 24 \times {10^5} \;
 \]
So by the calculation we got our result as \[24 \times {10^5}\]
Hence, the computer will take \[24 \times {10^5}\] seconds to calculate \[6,000,000,000,000\] calculations.
So, the correct answer is “ \[24 \times {10^5}\] seconds”.

Note: Now here to get the answer you should learn how to convert a number in scientific notation and what do we mean by scientific notation is to convert a very large number or very small number into a single digit multiplied by power of \[10\] . And the power could be negative as well. And then you should learn how to multiply two scientific terms. So when we multiply two terms which have power on it but the base is the same like \[{10^a} \times {10^b}\] then we will get \[{10^{a + b}}\] as our result.
Here you also have to be very careful with the sign of the power and add the power accordingly.