How to convert "433 kg" to "mg" in scientific notation?

Sep 11, 2016

see explanation

Explanation:

mg = milligram
$1 k g = 1 , 000 , 000 m g = 1 \times {10}^{6} m g$
$433 k g = 433 \times 1 \times {10}^{6} = 4.33 \times {10}^{8} m g$

Sep 11, 2016

"433 kg" = ?

Well, you can go from $\text{kg}$ to $\text{g}$ to $\text{mg}$ to make it easier. There's never any reason to skip steps, especially when you aren't comfortable yet...

$433 \cancel{\text{kg" xx (10^3 cancel"g")/cancel"kg" xx (10^3 "mg")/cancel"g}}$

$= 433 \times {10}^{6} \text{mg}$

$= \textcolor{b l u e}{4.33 \times {10}^{8} \text{mg}}$

Remember that scientific notation asks you to have the base number as $1. \overline{0} < x < 9. \overline{9}$. So slip that decimal point two magnitudes back.

$433 \times {10}^{6} \text{mg}$

$= 433 \times {10}^{8 - 2} \text{mg}$

$= 433 \times {10}^{- 2} \times {10}^{8} \text{mg}$

$= 4.33 \times {10}^{8} \text{mg}$