# How do we write 1347 in scientific notation?

Sep 14, 2016

$1347 = 1.347 \times {10}^{3}$

#### 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 $1347$ in scientific notation, we will have to move the decimal point three points to left, which literally means dividing by ${10}^{3}$.

Hence in scientific notation $1347 = 1.347 \times {10}^{3}$ (note that as we have moved decimal three points to left and thus divided by ${10}^{3}$, we are multiplying by ${10}^{3}$ to compensate

Sep 18, 2016

$1.347 \times {10}^{3}$

#### Explanation:

Building in steps so that you can see what is going on:

Given:$\text{ } 1347$

$1347 \equiv 134.7 \times 10$
$1347 \equiv 13.47 \times 10 \times 10$
$1347 \equiv 1.347 \times 10 \times 10 \times 10$

$1347 \equiv 1.347 \times {10}^{3}$