# How do you write 5,213 in scientific notation?

Feb 7, 2016

$5.213 \times {10}^{3}$

#### Explanation:

Your target is to have 1 digit (not 0) to the left of the decimal point and all the others to the right. In doing this on its own you are changing the value. So you have to mathematically correct this.

Given: $5213.000$

$\textcolor{b l u e}{\text{Step 1}}$

write as $5.213$

$\textcolor{b l u e}{\text{Step 2}}$

to change this back to the original number write it as:

$5.213 \times 1000$

$\textcolor{b l u e}{\text{Step 3}}$

Write 1000 as ${10}^{3}$ giving:

$5.213 \times {10}^{3}$

Feb 7, 2016

$5.213 \times {10}^{3}$

#### Explanation:

The form of a number in scientific notation is $a \times {10}^{n}$

where 1 ≤ a < 10 and n , is an integer

require to write 5 213 as a number between 1 and 10 so 5.213

to get this number back to what it should be , requires multiplying it by 1000.

hence 5.213 $\times 1000$

now 1000 = $10 \times 10 \times 10 = {10}^{3}$

$\Rightarrow 5213 = 5.213 \times {10}^{3}$