Question

Write $10000000000000$ in scientific notation.

Answer 1

Scientific notation of a number is the representation of numbers in such a way that very large numbers can be read easily without any discrepancy. Also in scientific notation the numbers are represented in the form $p \times {10^n}$ where $p$ should be between 1 and 10 i.e. $1 \leqslant p \prec 10$ and $n$ is an integer.
We can solve this question by using the above stated definition of scientific notation.

Complete step by step solution:
Given
$10000000000000..............................\left( i \right)$
So by the basic definition of scientific notation the numbers are represented in the form $p \times {10^n}$ where $1 \leqslant p \prec 10$and $n$ is an integer.
Such that we have to $p\;{\text{and}}\;n$ for the number $10000000000000$.
Now in order to find $p$ we have to move the position of decimal such that there is only a single digit before it.
So we get:
$\Rightarrow 10000000000000 = 1.0000000000000................\left( i \right)$
So we can write $p = 1$.
Now in order to find $n$ we have to determine the position of decimal which has been moved:
So here since it has been moved to the right side by $13$ positions, we can write:
$n = {10^{13}}........................\left( {ii} \right)$
If it had been left direction then the sign would be negative.
So from (i) and (ii) we can write:
$\Rightarrow p \times {10^n} = 1 \times {10^{13}} \\\ \Rightarrow 10000000000000 = 1 \times {10^{13}}..........\left( {iii} \right) \\\$
Therefore $10000000000000$ in scientific notation is $1 \times {10^{13}}$.

Note: To convert the general format numbers to scientific notation form certain rules have to be followed as given below:
1. The position of the decimal point should be such that there is only a single digit before it.
2. While moving the decimal points one should take care about the position which has been moved since it determines the power of 10.
3. Also the direction to which the decimal point has been moved is to be noted, if it has
been moved to left then the power is positive and if it’s moved to right then the power is negative.