Question

How do you write 0.0035 in scientific notation?

Answer 1

Hint: To write 0.0035 in scientific notation we are going to follow the following steps which are followed when we convert a number into scientific notation. The steps are we have to write the number in such a way so that it has two parts and these two parts are written in the product form. The first part of the number must lie in between 1 to 10 and the second part is some power of 10. Hence, we have to adjust the given number in such a manner so that the first part lies in between 1 to 10 and the power of 10 is adjusted in accordance with the first part.

Complete step by step solution:
The number given above in which we are asked to write the scientific notation is equal to:
0.0035
Now, in the first part we have to convert the above number in such a way so that it lies in between 1 to 10 so we are going to shift the decimal after 3 then the above number will look like:
3.5
As we have got the first part of the scientific notation but our number has been changed. The number has changed because the number which we have given is less than 1 and the number we have converted is greater than 1 so we have to multiply this number by some power of 10 to adjust the decimal. We have shifted 3 numbers from the original position of the decimal so we are going to put -3 as the power of 10.
Multiplying ${{10}^{-3}}$ to 3.5 we get,
$3.5\times {{10}^{-3}}$

From the above, the scientific notation for the given number as follows:
$3.5\times {{10}^{-3}}$.

Note: The mistake that could be possible in the above problem is in writing the power of 10. The plausible mistake lies in whether positive or negative power should be there so the trick to correct this mistake is that:
When you shift decimal in the forward direction of a number just as we did in the above problem that we have shifted decimal from 0.0035 to 3.5 then the power of 10 which we multiply is negative.
And when we shift decimal in the reverse direction say if we have a number 32.6 then shifting of decimal in the reverse direction is from 32.6 to 0.326. Now, the power of 10 which we multiply to is the positive power of 10 i.e. ${{10}^{2}}$.