# How do you write 0.0045 in scientific notation?

Jun 10, 2016

$0.0045 = 4.5 \times {10}^{- 3}$

#### 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 $0 , 0045$ in scientific notation, we will have to move the decimal point three point to right, which literally means multiplying by $1000 = {10}^{3}$.

Hence in scientific notation $0.0045 = 4.5 \times {10}^{- 3}$ (note that as we have moved decimal three point to right we are multiplying by ${10}^{- 3}$.