# How do you write 42,000 in scientific notation?

Aug 30, 2016

$4.2 \times {10}^{3}$

#### Explanation:

These take a little bit of getting used to.

Multiply by 1 and you do not change the inherent value. 1 can be written in many ways. So you can change the way something looks without changing its inherent value.

Example: multiply 3 by 1 but in the form of $1 = \frac{4}{4}$

$3 \times \frac{4}{4} = \frac{3 \times 4}{4} = \frac{12}{4}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The objective is to have just 1 non zero value to the left of the decimal point and everything else to its right.

Given:$\text{ } 42000$

Multiply by 1 but in the form of $1 = \frac{10000}{10000}$

$42000 \times \frac{1000}{1000}$

$\frac{42000}{1000} \times 1000$

$4.2 \times 1000$

But $1000$ is the same as ${10}^{3}$

So $4.2 \times 1000 \text{ "->" } 4.2 \times {10}^{3}$