Question

How do you write $20,000$ in scientific notation?

Answer 1

Hint: In this question, we have been given a number and we have been asked to write the number in scientific notation. At first, read what scientific notation is and then, break the given number in a way that all the tens are separated. Then, raise the tens to their powers in order to simplify them.

Formula used: A number, $x$ can also be written as –
$x = a \times {10^p}$

Complete step-by-step solution:
We are given a number and we have been asked to write the number in scientific notation.
What is scientific notation?
Scientific notation is a way of writing numbers either very small or very large numbers in a simpler form. It is also known as standard index form. The proper format for scientific notation is - $x = a \times {10^p}$, where $x$ is the given number and $a$ is a number greater than or equal to $1$ , but less than $10$, and $p$ can either be negative or positive, denoting that whether the number is in decimals or not.
Now, moving towards the question,
We are given a number - $20,000$.
We can write the number as - $2 \times 10,000$
Observe that our $a = 2$ and $1 \leqslant 2 < 10$ .
Hence, it lies in the required interval.
Now, we can write $10,000$ as ${10^4}$ .
Hence, $20,000 = 2 \times 10,000 = 2 \times {10^4}$

Therefore, our required scientific notation is $2 \times {10^4}$ .

Note: In case the number given to us had been in decimals, the power would have been negative. Let us take an example.
For example, Convert $0.0002$ into scientific notation.
At first, we will convert the number into fractions –
$ \Rightarrow 0.0002 = \dfrac{2}{{10,000}}$
We can rearrange the number as –
$ \Rightarrow \dfrac{2}{{10,000}} = 2 \times \dfrac{1}{{10,000}}$
Now, using properties of exponents, we can write $\dfrac{1}{{10,000}} = 10,{000^{ - 1}}$
Also, we know that $10,000$ can be written as ${10^4}$ .
Hence, $\dfrac{1}{{10,000}} = {\left( {{{10}^4}} \right)^{ - 1}}$
We know that ${\left( {{a^b}} \right)^c} = {a^{bc}}$ .
Hence, $\dfrac{1}{{10,000}} = {10^{ - 4}}$
Therefore, $0.0002 = 2 \times {10^{ - 4}}$