# How do you convert mm to cm, and kg to mg in metric system?

Jul 19, 2017

It's easy enough once you understand the prefixes. It is typically just multiplying and dividing by tens, thousands, millions etc.

#### Explanation:

In short: because there are 10 mm in each cm, the number will go down by a factor of 10 (thus 47.3 mm = 4.73 cm)

Similarly in 1 kg there are 1000 g hence 1000 000 mg so the number will increase by a factor of 1 million (2.7356 kg = 2735 600 mg)

Fundamentally, you need to understand SI prefixes here and then how to use standard form here and you're good to go. One final point, the c prefix as in cm is not formally part of the Système Internationale (SI) but is very common as a centimetre is such a useful scale for us humans.

Jul 19, 2017

Well $\text{milli} = {10}^{-} 3$......

#### Explanation:

...and thus $1 \cdot m m \equiv 1 \times {10}^{-} 3 \cdot m$

But $\text{centi} \equiv {10}^{-} 2$....and thus $1 \cdot c m \equiv {10}^{-} 2 \cdot m \equiv 10 \cdot m m$

On the other hand $k \equiv {10}^{3}$, and $m \equiv {10}^{-} 3$ (remember that I am ALSO using the abbreviation $\text{m "-=" metre}$.)

And $1 \cdot k g \equiv 1 \times {10}^{3} \cdot g$, and $1 \cdot m g \equiv 1 \times {10}^{-} 3 \cdot g$.

And so $1 \cdot g \equiv 1000 \cdot m g$, and $1 \cdot k g \equiv 1000 \cdot g = {10}^{6} \cdot m g$.

All I am doing is using the multipliers.......(hopefully appropriately)

$\text{micro} \equiv {10}^{-} 6$, $\text{milli} \equiv {10}^{-} 3$, $\text{centi} \equiv {10}^{-} 2$, $\text{deci} \equiv {10}^{-} 1$, $\text{kilo} \equiv {10}^{3}$.

One usage that is quite common in the UK is the use of ${\mathrm{dm}}^{3}$ for volume, in preference to $\text{litres}$. Now $1 \cdot {\mathrm{dm}}^{3} \equiv 1 \cdot L$, but ${10}^{3} \cdot L = 1 \cdot {m}^{3}$, and .............$1 \cdot {\mathrm{dm}}^{3} \equiv {\left(1 \times {10}^{-} 1 \cdot m\right)}^{3} = {10}^{-} 3 \cdot {m}^{3} = 1 \cdot L$ as required.

So how do you remember them? Keep practising, and note your mistakes. We all make mistakes.