# Multiplying mass as kg and grams= 2 different results?

1. Aug 6, 2015

### christian0710

Hi, I'm just wondering. If you mulitiply 1kg with 0.5kg you get 0.5kg

But if you do the multiplication in grams you get
1000g *500g = 500.000g = 500kg. a dompletely different result.

Why is that? How do you avoid this problem?

2. Aug 6, 2015

### e.bar.goum

No, when you multiply 1kg with 0.5 kg you get 0.5 kg2 - square kilograms. You must also multiply the units!

1000g *500g = 500 000 g2

Now, to convert square kilograms to square grams,

1kg * 1kg = 1000 g * 1000 g = 1 000 000 g2

So, now we take 500 000/ 1 000 000 g2 = 0.5 kg2. Precisely the same result.

3. Aug 6, 2015

### ShayanJ

$1 \ kg \ \times \ 0.5 \ kg=0.5 \ (kg)^2=0.5 \ \times \ 10^6 \ g^2$
$1000 \ g \ \times \ 500 \ g=0.5 \ \times \ 10^6 \ g^2$

4. Aug 6, 2015

### Staff: Mentor

Without any context, I can't think of any reason you would want to multiply two quantities in kilogram units.

As already posted, the units of the product would be kg2, which by itself isn't very meaningful.