Question

How do you write 634, 000 in scientific notation?

Answer 1

Hint: To write a given number into scientific form, we have to write the number in such a manner so that it has two parts which 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 so 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 which we have to write the scientific notation is as follows:
634, 000
So, let us write the scientific by putting decimal to it so that the number will lie in between 1 to 10. If we put decimal between 6 and 3 then the number will lie in between 1 to 10.
6.34000
From the above, you can see that we have 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 5 numbers from the last number so we have to write 5 as the power of 10.
Multiplying ${{10}^{5}}$ to 6.34000 we get,
$\Rightarrow 6.34\times {{10}^{5}}$
From the above, the scientific notation for the given number as follows:
$\Rightarrow 6.34\times {{10}^{5}}$

Note: The mistake that could be possible in the above problem is that you might get confused whether to put a positive power or a negative power to the number 10. Then the answer to this confusion is that whenever you shift the decimal towards the starting digit of a number then you will put the positive power of 10 just like we did in the above problem and whenever we shift the decimal to the direction in which the number ends then you have to put negative power of 10.
In the below, we are showing the negative power of 10:
Let us say, we have a number say 2.345000. Now, shifting the decimal towards the last digit of this number we have:
$\Rightarrow 234500.0$
As we have shifted the decimal 5 places from the original position in the forward direction so we have to put the negative power of 5 to the number 10.
$\Rightarrow 234500.0\times {{10}^{-5}}$