Question

How do you write 21000000 in scientific notation?

Answer 1

Hint: The purpose of scientific notation was developed in order to easily represent numbers that are either very large or very small. We use the decimal point and move it leftwards. To compensate for that we have to multiply the new number by 10. The multiplied form is the scientific form of the given number.

Complete step by step answer:
The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.
We move the decimal to the smallest one-digit place so that it can be expressed in the multiplication form of 10. For 21000000 we keeping moving the decimal to the left. The decimal starts from the last zero in 21000000. We multiply with 10 to compensate for the movement.
We explain the first two steps. The decimal starts after then last zero in 21000000.
Now it goes before the last zero in 21000000. The number changes from 21000000 to 2100000. This means we have to multiply 10.
So, 21000000 becomes \[2100000.0\times 10\].
Now in the second step, the point crosses two zeroes in total which gives \[210000.00\times {{10}^{2}}\].
We go on like this till the decimal point has only one digit to cross to go to the leftmost position of the number.
In 21000000, the movement of the decimal point happens 7 times which means \[2.1000000\times {{10}^{7}}\].
Therefore, the scientific notation of 21000000 is \[2.1000000\times {{10}^{7}}\].

Note:
 We also can ignore the zeroes after decimal points and make the notation as \[2.1\times {{10}^{7}}\] for simplicity and mathematical use. The use of \[2.1000000\] is unnecessary. But in cases we have non-zero digits after 0 after the decimal, we can’t ignore those zeroes.