# How do I convert 3427 into scientific notation?

Oct 11, 2014

A number in scientific notation is in the form

$a \cdot {10}^{b}$

Generally,

$1 \le a < 10$

For $3427$, the decimal point is on the right of 7

$3427.0$

We need to move the decimal such that $1 \le a < 10$ will be satisfied.

However, we also need to retain its value.
For each movement of the decimal place to the left, multiply the number by 10.

To satisfy $1 \le a < 10$, the decimal place needs to move by 3 places to the left.

Hence, we have

$3.427 \cdot {10}^{3}$

For the longer version of converting to scientific notation, we have
$3427 \cdot \left(1\right) = 3427$
$3427 \cdot \left(\frac{1}{10} \cdot 10\right) = 3427$
$\left(3427 \cdot \frac{1}{10}\right) \cdot 10 = 3427$
$342.7 \cdot 10 = 3427$

$342.7 \cdot 1 \cdot 10 = 3427$
$342.7 \cdot \left(\frac{1}{10} \cdot 10\right) \cdot 10 = 3427$
$\left(342.7 \cdot \frac{1}{10}\right) \cdot \left(10 \cdot 10\right) = 3427$
$34.27 \cdot \left({10}^{2}\right) = 3427$

$34.27 \cdot 1 \cdot \left({10}^{2}\right) = 3427$
$34.27 \cdot \left(\frac{1}{10} \cdot 10\right) \cdot \left({10}^{2}\right) = 3427$
$\left(34.27 \cdot \frac{1}{10}\right) \cdot \left(10 \cdot {10}^{2}\right) = 3427$
$3.427 \cdot {10}^{3} = 3427$