Question

How do you write 0.02 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. 0.02.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 and greater than 1. Therefore, we shall move the decimal point towards right by 2 decimal places so that the new number can be written as 2 and then we shall multiply the new number by ${{10}^{-2}}$. With this, the number 0.02 can be written as $2\times {{10}^{-2}}$.

Hence, we wrote the scientific notation for the given number.

Note: The value of N cannot be equal to 10 or -10. When the given number is greater than 1 and multiples of 10, the decimal point is moved towards the left. If we move the decimal point towards the left by ‘p’ places then we have to multiply the new number by factor of ${{10}^{p}}$.