# How do you write the number in scientific notation 5,100,000?

Nov 25, 2016

$5 , 100 , 000 = 5.1 \times {10}^{6}$

#### 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 $5 , 100 , 000$ in scientific notation, we will have to move the decimal point six points to left, which literally means dividing by ${10}^{6}$.

Hence in scientific notation $5 , 100 , 000 = 5.1 \times {10}^{6}$ (note that as we have moved decimal six points to left, we are multiplying by ${10}^{6}$ to compensate for division by ${10}^{6}$.