Question

How do you write $0.00000000318$ in standard notation?

Answer 1

Hint: We have been given a very small number and we can decipher this because of the large number of zeros given after the decimal point. Thus, we shall first carefully count the number of zeroes, put the decimal point only after one digit and accordingly assign a positive or negative power to 10 in order to write the given number in standard notation.

Complete step-by-step answer:
The standard notation of any figure follows certain rules. The decimal point comes after one digit only. Rest of the digits are placed after the decimal point and the zeroes are represented as 10 raised to some negative or positive number.
We have been given the number, $0.00000000318$. On carefully counting, we get that there are 11 digits after the decimal point. But we need only one significant digit before the decimal point, therefore. We must take the decimal point 9 digits towards the right and then balance the zeroes by raising 10 to the power of $-9$, (because the decimal point was dragged eight digits towards the right).
Therefore, we get the standard notation is given as $3.18\times {{10}^{-9}}$.

Note:
In any kind of science, we deal with very large numbers like the number of atoms in our body as well as very small numbers like the mass of an atom. Such numbers which are either very large or very small also become unreadable. Looking at the huge number of zeros before or after the decimal point also makes the mathematical figures unreadable. The possible mistake one can make is writing +9 instead of -9 as the power of 10. So, we have to be very careful while solving.