Question

How do you convert $45700$ into scientific form?

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 with 10. The multiplied form is the scientific form of the given number.

Complete step-by-step solution:
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 $45700$, we keep moving the decimal to the left. The decimal starts after the last zero in $45700$. We multiply with 10 to compensate for the movement. We go on till the decimal has one digit to cross.
We explain the first two steps. The decimal starts after the last zero in $45700$.
Now it goes before the last zero in $45700$. The number changes from $45700$to $4570$. This means we have to multiply 10.
So, $45700$ becomes \[4570.0\times 10\].
Now in the second step the point crosses two zeroes in total which gives \[457.00\times {{10}^{2}}\].
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 $45700$, the movement of the decimal point happens 4 times which means \[4.5700\times {{10}^{4}}\].
Therefore, the scientific notation of $45700$ is \[4.57\times {{10}^{4}}\].

Note: We have to ignore the zeros after decimal points and make the notation as \[4.57\times {{10}^{4}}\] for the simplicity and mathematical use. The use of \[4.5700\] is unnecessary. But in cases we have non-zero digits after 0 after decimal, we can’t ignore those zeroes.