# How do you write 673.5 in scientific notation?

Jun 12, 2017

To write the expression in scientific notation we need to move the decimal point 2 places to the left so the exponent for the 10s term will be positive:

$673.5 = 6.735 \times {10}^{2}$

Jun 12, 2017

$6.735 \cdot {10}^{2}$

#### Explanation:

By definition, scientific notation is expressed in a form of

$a \cdot {10}^{n}$ where $10 > a > 1$ and $n$ is an integer.

Using this definition, we can form $a$ by expressing it as $6.735$ multiplied by a power of $10$. But what power of $10$ should we multiply it by?

What this is really asking is

$6.735 \cdot {10}^{n} = 673.5$

Well that's easy! $6.735$ multiplied by $100$ is $673.5$! And since $100$ is ${10}^{2}$, we can now write our scientific notation expression!

$6.735 \cdot {10}^{2}$