# How do we write 50000 in scientific notation?

Sep 15, 2016

$50000 = 5 \times {10}^{4}$

#### Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of $10$.

Note that moving decimal $p$ digits to right is equivalent to multiplying by ${10}^{p}$ and moving decimal $q$ digits to left is equivalent to dividing by ${10}^{q}$.

Hence, we should either divide the number by ${10}^{p}$ i.e. multiply by ${10}^{- p}$ (if moving decimal to right) or multiply the number by ${10}^{q}$ (if moving decimal to left).

In other words, it is written as $a \times {10}^{n}$, where $1 \le a < 10$ and $n$ is an integer.

To write $50000$ in scientific notation, we will have to move the decimal point four points to left, which literally means dividing by ${10}^{4}$.

Hence in scientific notation $50000 = 5 \times {10}^{4}$ (note that as we have moved decimal four points to left and thus divided by ${10}^{4}$, we are multiplying by ${10}^{4}$ to compensate.

Sep 18, 2016

$5.0 \times {10}^{4}$

#### Explanation:

Built in stages so that you can see what is happening

$50 , 000 \to 5000 \times 10$

$50 , 000 \to 500 \times 10 \times 10$

$50 , 000 \to 50 \times 10 \times 10 \times 10$

$50 , 000 \to 5 \times 10 \times 10 \times 10 \times 10$

Thus: $50 , 000 \equiv 5.0 \times {10}^{4}$