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 $1⩽2<10$ .
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 –
$\Rightarrow 0.0002={\displaystyle \frac{2}{10,000}}$
We can rearrange the number as –
$\Rightarrow {\displaystyle \frac{2}{10,000}}=2\times {\displaystyle \frac{1}{10,000}}$
Now, using properties of exponents, we can write ${\displaystyle \frac{1}{10,000}}=10,{000}^{-1}$
Also, we know that $10,000$ can be written as ${10}^4$ .
Hence, ${\displaystyle \frac{1}{10,000}}={\left({10}^4\right)}^{-1}$
We know that ${\left(a^b\right)}^c=a^{bc}$ .
Hence, ${\displaystyle \frac{1}{10,000}}={10}^{-4}$
Therefore, $0.0002=2\times {10}^{-4}$