Question

How do you write $3.14\times {{10}^{-6}}$ in expanded form?

Answer 1

Hint: We have been given a very small number and we can decipher this because of the large negative power of -6 on base 10. We have to convert this from the given standard notation to the expanded form. Thus, we shall carefully count the number of zeroes and put them after the decimal point in order to expand this small number given.

Complete step-by-step solution:
We have been given the number, $3.14\times {{10}^{-6}}$. On careful observation, we understand we have to multiply and divide the number by ${{10}^{6}}=1000000$.
$\Rightarrow 3.14\times {{10}^{-6}}=3.14\times {{10}^{-6}}\times \dfrac{{{10}^{6}}}{{{10}^{6}}}$
$\Rightarrow 3.14\times {{10}^{-6}}=\dfrac{3.14}{1000000}$
In order to simplify this expression, we must take the decimal point 6 digits towards the left. Thus, we shall take the digit 3 to the right-hand side of the decimal point and also add 5 zeros on the right-hand side of the decimal point to balance the number $1000000$ in the denominator.
$\Rightarrow 3.14\times {{10}^{-6}}=0.00000314$
Therefore, we get that the expanded form is given as $0.00000314$.

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 4 or 6 zeroes instead of 5 as the power of 10. So, we have to be very careful while solving.