# How do you express 0.096 in scientific notation?

Aug 6, 2016

$0.096 = 9.6 \times {10}^{- 2}$

#### 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 $0.096$ in scientific notation, we will have to move the decimal point two points to right, which literally means multiplying by ${10}^{2}$.

Hence in scientific notation $0.096 = 9.6 \times {10}^{- 2}$ (note that as we have moved decimal two points to the right, we are multiplying by ${10}^{2}$ and hence to compensate we should divide by ${10}^{2}$ i.e. multiply by ${10}^{- 2}$).