Confusing powers

thecatspjs

Is 0.27x10^-6 meters cubed the same as 0.27 cm cubed?
Just doin some problems here and can't get my head around this for some reason

FarmerGreen

0.27 micrometers? 10^-6= one millionth.

Michael Collins

thecatspjs wrote: »

Is 0.27x10^-6 meters cubed the same as 0.27 cm cubed?
Just doin some problems here and can't get my head around this for some reason

Yes,

[latex] \displaystyle 0.27 \times 10^{-6} \cdot \hbox{m^3} [/latex]

100 cm in every m, so

[latex] \displaystyle 0.27 \times 10^{-6} \cdot (100 \; \hbox{cm})^3 [/latex]

[latex] \displaystyle 0.27 \times 10^{-6} \cdot (100^3 \; \hbox{cm}^3) [/latex]

[latex] \displaystyle 0.27 \times 10^{-6} \cdot 10^6 \; \hbox{cm}^3 [/latex]

[latex] \displaystyle 0.27 \; \hbox{cm^3} [/latex]

FISMA

Do you want to cube the whole lot - [0.27x10^-6 meters]^3?

[0.27x10^-6 meters]^3 = 1.97x10-14 cm^3

But if you meant to convert [0.27x10^-6 ] meters^3? to cm^3 then as demonstrated by the Big Fella

[0.27x10^-6 ] meters^3? = 0.27cm^3 - true because in one cubic meter there are one million centimeter sized cubes.

FarmerGreen

thecatspjs wrote: »

Is 0.27x10^-6 meters cubed the same as 0.27 cm cubed?

Without the cubed,
Is 0.27x10^-6 meters the same as 0.27 cm ?

Greenmachine

Michael Collins wrote: »

Yes,

[latex] \displaystyle 0.27 \times 10^{-6} \cdot \hbox{m^3} [/latex]

100 cm in every m, so

[latex] \displaystyle 0.27 \times 10^{-6} \cdot (100 \; \hbox{cm})^3 [/latex]

[latex] \displaystyle 0.27 \times 10^{-6} \cdot (100^3 \; \hbox{cm}^3) [/latex]

[latex] \displaystyle 0.27 \times 10^{-6} \cdot 10^6 \; \hbox{cm}^3 [/latex]

[latex] \displaystyle 0.27 \; \hbox{cm^3} [/latex]

What? surely 0.27x10^-4 meters = 0.27 cm

FarmerGreen

FarmerGreen wrote: »

Without the cubed,
Is 0.27x10^-6 meters the same as 0.27 cm ?

The 0.27 thing.
Is a millionth the same as a hundredth.
Hugely confused Ted.

FISMA

FarmerGreen wrote: »

Without the cubed,
Is 0.27x10^-6 meters the same as 0.27 cm ?

10^-6 is a "micro" - one millionth
10^-2 is a "centi" - one hundreth

So, the two cannot be equal.

0.27x10^-6m = 0.00000027m = 0.000027cm

Greenmachine wrote: »

What? surely 0.27x10^-4 meters = 0.27 cm

First break up the power
0.27x10^-4 m = 0.27 x 10^-2 x 10^-2 m,

Call the 10^-2 what it is - "centi" and replace one of the above

0.27x10^-4 m = 0.27 x 10^-2 x 10^-2 m = 0.27 x 10^-2 centi*m

So we have
0.27x10^-4 m = 0.0027cm = 0.000027m = 0.27x10-2cm

FarmerGreen

Go on!
Say it.
Oops.

FISMA

FarmerGreen wrote: »

Go on!
Say it.
Oops.

I prefer d'Oh!

I never did like powers or conversions, especially adding them - 8.7E-2 + 2.3E-5...

Greenmachine

FISMA wrote: »

I prefer d'Oh!

I never did like powers or conversions, especially adding them - 8.7E-2 + 2.3E-5...

I had to look at your post a few times to work through it. Was confused at the two answer till I realised you were solving two different problems.