Question

How do you write 0.007 in scientific notation?

Answer 1

We are asked to convert 0.007 in scientific notation. And we know that to convert a number into scientific notation, 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 be 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 answer:
The number given in the above problem which we are asked to write the scientific notation is equal to:
0.007
Now, first of all, we are going to convert the number by shifting the decimal after 7 from the decimal which is written just after the first 0. We are doing this shifting of the decimal so that our first part should lie in the range of 1 to 10.
7.0
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 7 and the number we have converted is greater than 7 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 7.0 we get,
$\Rightarrow 7.0\times {{10}^{-3}}$
From the above, the scientific notation for the given number as follows:
$\Rightarrow 7.0\times {{10}^{-3}}$

Note: You can check the scientific notation that you have written for the given number is correct or not as follows:
The trick to check the scientific notation is by multiplying ${{10}^{-3}}$ to 7.0. When we multiply the negative power of 10 to a decimal then decimal will be shifted backwards in respect to the power of 10. As the power of 10 is -3 so the decimal will be shifted 3 numbers in backward direction from its original position. Then the number that we will get is:
0.007
As no number is written before 7 so we have taken 0 before 7 in the above.
From the above, we got the same number as we have started with so hence,the scientific notation that we have written is correct.