Help with simple secondary school Physics question.

[iZH]

Homework Statement

Convert the number below by giving the answer in standard form.

Homework Equations

1) 0.0012m(to the power of 2) = _____ cm(to the power of 3)
2) 12kmh(to the power of -1) = _____ ms(to the power of -1)
3) 12ms(to the power of -1) = _____ kmh(to the power of -1)

My effort of showing that i tried.
1)2)3) i convert the number to cm/ms/kmh first. then change it to standard form, but i still don't get what the question really want, and what is the step required. And the answer look really strange. I've been trying this for the whole afternoon until now.

P/S I saw a lot of complicated question being asked here, but i am new to Physics, and currently stuck at my Physics Chapter 1 homework which is a secondary school standard.
Hope i get a proper formula with answer ASAP. Thanks T_T

 

[vela]

Do you have a typo in the first problem? What do you mean by "standard form"?

 

[iZH]

well, typo for grammar is a yes i guess. But not "standard form" i think.

Kay, i'll give you an easier example that i know.
Convert the number below and write the answer in standard form.
(A) 7.2m to cm
So, it's 720cm after converted. And so, the answer in standard form are,
7.2 x 10(to the power of) -2 cm

Yes, if my post confused you, I'm sorry for the inconvenient caused. Because this is what i learned recently, and I'm new to this forum.Edited*
Oh yeah, another name for "Standard Form" is called the "Scientific Notation".
-Standard form is based on powers of base number 10. In standard form, the magnitude or numerical value of physical quantity can be written as:

A x 10 (to the power of) x

 

[vela]

OK, that's what I thought you meant by "standard form". The typo I'm referring to are the powers in the first problem. There's no way to convert m² to cm³.

 

[iZH]

Yes, that's one of the problem that i don't understand too, if you say so, then i guess maybe it's my teacher's mistake for the powers typo.
Thanks for pointing that out.

But do you have any ideas on how to solve the 2nd and 3rd question?

 

[vela]

OK, you have 12 km/h and you want to convert it to m/s. First, note that

$$1~\mbox{km} = 1000~\mbox{m} \rightarrow \frac{1000~\mbox{m}}{1~\mbox{km}} = 1$$

Since multiplying by 1 doesn't change anything, you have

$$12 \frac{\mbox{km}}{\mbox{h}} = 12 \frac{\mbox{km}}{\mbox{h}}\times \frac{1000~\mbox{m}}{1~\mbox{km}}$$

Now the km in the numerator of the first factor cancels with the km in the denominator of the second, leaving you with

$$12 \frac{\mbox{km}}{\mbox{h}} = 12000 \frac{\mbox{m}}{\mbox{h}}$$

You do the same sort of thing to change the h in the bottom to s, using the conversion factors

$$1~\mbox{h} = 60~\mbox{min}$$

$$1~\mbox{min} = 60~\mbox{s}$$

 

[iZH]

Yes, thanks.
And my answer are 12000m/3600s
The question said, i need to change it to standard form.
Do you have any idea on how to convert 12000m/3600s to standard form?
This is the part which i actually stuck at.

By using scientific calculator, my calculator showed this
12000m/3600s = 3.33333 which is endless.
I found this is the wrong way to solve the question.

So i gave my try on the second method in mind.
converting 12000m to standard form give me 1.2 x 10(to the power of)4
converting 3600s to standard form give me 3.6 x 10(to the power of)3
Now I'm stuck at this step again.
1.2 x10(to the power of)4 / 3.6 x 10(to the power of)3
I can't seems to give the answer in standard form as i think this is the wrong way too.

So, any ideas on how to change the answer to standard form?

 

[vela]

You just have to truncate the number at the correct number of significant figures. The original figure was 12 km/h, which has two significant figures, so the answer would be 3.3 m/s. If it had been 12.00 km/h, you'd write 3.333 m/s.

You don't need to include a power of 10 when the exponent would be zero.

 

[iZH]

Ok, i get it now. Thanks for every effort you put in this thread :) Appreciate your help so much. ^^