Question

How do you write 0.00357 in scientific notation ?

Answer 1

Hint: Scientific notation is a method to write some numbers in a specific and convenient form. This method is mostly used for the numbers (may be decimal numbers) that are very small or very big. Know the general form of scientific notation and write the scientific notation for the given number.

Complete step by step solution:
Let us first understand what is meant by scientific notation.
Scientific notation is a method to write some numbers in a specific and convenient form. This method is mostly used for the numbers (may be decimal numbers) that are very small or very big. This makes our job easier as the many digit numbers are shortened to a very less digit number. Let us now see how it is done.

The scientific notation of any number is given as $N\times {{10}^{m}}$, where N is any real number between 1 to 10 or -10 to -1 and m is an integer (it can take any value of integer).Let us write the scientific notation for the given number, i.e. 0.00357.We know that each successive digit after the decimal represents multiplication of ${{10}^{-1}}$. This means that we can move the decimal point towards right by ‘p’ places and multiply the new number by ${{10}^{-p}}$.

We also must keep in mind that the number N must between less than 10. Therefore, we shall move the decimal point towards right by 3 decimal places so that the new number can be written as 3.57 and then we shall multiply the new number by ${{10}^{-3}}$. With this, the number 0.00357 can be written as $3.57\times {{10}^{-3}}$.Hence, we wrote the scientific notation for the given number.

Note:We will also do the following for writing the number in scientific notation.
We can multiply and divide the number by ${{10}^{3}}$. Then this gives us that
$0.00357=0.00357\times \dfrac{{{10}^{3}}}{{{10}^{3}}}$.
We can write $0.00357\times {{10}^{3}}=3.57$ and $\dfrac{1}{{{10}^{3}}}={{10}^{-3}}$.
Therefore, the scientific notation of the number is $3.57\times {{10}^{-3}}$.