Question

How do you write 640,000,000,000,000 in scientific notation?

Answer 1

Hint: To write the number given in the above problem into scientific form, we have to write the number in such a way so that it will contain two parts and that too are written in the product form. The first part of the number should lie in between 1 to 10 and the second part contains some power of 10. And the catch is that we have to adjust the given number in such a way so that the first part lies in between 1 to 10 and the power of 10 is adjusted according to the first part.

Complete step by step answer:
The number given in the above problem of which we have to write the scientific notation is as follows:
640,000,000,000,000
So, we are going to convert the above number by putting the decimal first to it so that the number will lie in between 1 to 10. If we put decimal between 6 and 4 then the number will lie in between 1 to 10.
6.40,000,000,000,000
As you can see, we successfully got the first part of the scientific notation but our number has been changed so we have to multiply this number by some power of 10 to adjust the decimal. We have put decimal 14 numbers from the last number so we have to write 14 as the power of 10.
Multiplying ${{10}^{14}}$ to 6.40,000,000,000,000 we get,
\[\Rightarrow 6.4\times {{10}^{14}}\]
From the above, the scientific form for the given number as follows:
\[\Rightarrow 6.4\times {{10}^{14}}\]

Note: The possible mistake in the above problem is that you might miss the exact power of 10 which comes when we adjusted the decimal which we have put in the first part of the scientific notation. The reason being there are so many zeros in the given number so make sure you have carefully counted the zeros and then will write the power of 10. And this mistake can be checked out by the following trick: The trick to check the scientific notation is by multiplying ${{10}^{14}}$ to 6.40, 000, 000, 000, 000
. When we multiply the positive power to a decimal then decimal will be shifted with respect to the power of 10. As the power of 10 is 14 so the decimal will be shifted 7 numbers from its original position. Then the number that we will get is:
6.40, 000, 000, 000, 000.0
We know that 0 after decimal is not significant so we can write the above number as:
6.4