The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

Converting gcm^-3 to kgm^-3

Howdy :smile:.


Screen Shot 2017-07-20 at 16.00.47.png

I don't understand question. If it had positive indices then I can see that m^3 is 100 x 100 x 100.

I get how to get to the answer of 5000 kgm^-3 but I don't get what the m^-3 is used for and how I can use the 100 x 100 x 100 rule for cm^-3.

Where is m^-3 used (this is out of as level mechanics book).

Hope that makes sense.

Thanks
Original post by makin
Howdy :smile:.


I don't understand question. If it had positive indices then I can see that m^3 is 100 x 100 x 100.

I get how to get to the answer of 5000 kgm^-3 but I don't get what the m^-3 is used for and how I can use the 100 x 100 x 100 rule for cm^-3.

Where is m^-3 used (this is out of as level mechanics book).

Hope that makes sense.

Thanks


Well if m3=(100×100×100)cm3\mathrm{m}^3=(100 \times 100 \times 100) \mathrm{cm}^3 then m−3=1100×100×100cm−3\mathrm{m}^{-3}=\frac{1}{100 \times 100 \times 100} \mathrm{cm}^{-3}

So 1003m−3=cm−3100^3 \mathrm{m}^{-3} = \mathrm{cm}^{-3}

Hence you can express 5g cm−35\mathrm{g \ cm}^{-3} as 5g⋅1003m−35\mathrm{g} \cdot 100^3 \mathrm{m}^{-3} thus 5,000,000g m−35,000,000 \mathrm{g \ m}^{-3}

And since g=0.001kg\mathrm{g}=0.001 \mathrm{kg} we have 5,000,000⋅0.001kg m−35,000,000 \cdot 0.001 \mathrm{kg \ m}^{-3} which gives the answer. Get it?
5 g cm^-3 = (5 x 10^-3 kg) (10^-2 m)^-3
= (5 x 10^-3 x 10^6) kg m^-3
= (5 x 10^3) kg m^-3
= 5000 kg m^-3

No need to memorise rules, just manipulate powers.
Reply 3
Avatar for makin
makin
OP
9
Original post by RDKGames
Well if m3=(100×100×100)cm3\mathrm{m}^3=(100 \times 100 \times 100) \mathrm{cm}^3 then m−3=1100×100×100cm−3\mathrm{m}^{-3}=\frac{1}{100 \times 100 \times 100} \mathrm{cm}^{-3}

So 1003m−3=cm−3100^3 \mathrm{m}^{-3} = \mathrm{cm}^{-3}

Hence you can express 5g cm−35\mathrm{g \ cm}^{-3} as 5g⋅1003m−35\mathrm{g} \cdot 100^3 \mathrm{m}^{-3} thus 5,000,000g m−35,000,000 \mathrm{g \ m}^{-3}

And since g=0.001kg\mathrm{g}=0.001 \mathrm{kg} we have 5,000,000⋅0.001kg m−35,000,000 \cdot 0.001 \mathrm{kg \ m}^{-3} which gives the answer. Get it?


Yes, thanks :biggrin:.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you