# How do you write 1,240,000,000 in scientific notation?

Nov 3, 2016

$1 , 240 , 000 , 000 = 1.24 \times {10}^{9}$

#### 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 $1 , 240 , 000 , 000$ in scientific notation, we will have to move the decimal point nine points to the left, which literally means dividing by ${10}^{9}$.

Hence in scientific notation $1 , 240 , 000 , 000 = 1.24 \times {10}^{9}$ (note that as we have moved decimal nine points to left we are multiplying by ${10}^{9}$ to compensate for dividing by ${10}^{9}$.
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