# How do you write 405,000 in scientific notation?

Mar 3, 2017

$405 , 000 = 4.05 \times {10}^{5}$

#### 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 $405 , 000$ in scientific notation, we will have to move the decimal point five points to left, which literally means dividing by ${10}^{5}$.

Hence in scientific notation $405 , 000 = 4.05 \times {10}^{5}$ (note that as we have moved decimal one point to right we are multiplying by ${10}^{5}$ to compensate for division by ${10}^{5}$ due to shifting of decimal poimt.