# How do we write 10345089.41 in scientific notation?

Sep 18, 2016

$10345089.41 = 1.034508941 \times {10}^{7}$

#### 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 $10345089.41$ in scientific notation, we will have to move the decimal point seven points to left, which literally means dividing by ${10}^{7}$.

Hence in scientific notation $10345089.41 = 1.034508941 \times {10}^{7}$ (note that as we have moved decimal seven points to left we are multiplying by ${10}^{7}$ to compensate for division by ${10}^{7}$.