Expressing measurements in SI units

[RabbitWho]

Homework Statement

I am given some measurements and I am supposed to express them as standard SI units. I can't find any examples of this done online or extra practice exercises to help me. I am probably googling the wrong words.
I have been out of school for quite a while and I don't know what some of the abbreviations stand for, and a lot of letters seem to double up in physics.

105km
57mm
6.67x10^-11cm
6x10²⁷ grams
9 grams per cubic centimetre
100 km h^-1
5 nN
10μW
5Gm

I don't know what G, or μ or h (hour?) stand for here.

Homework Equations

3. The Attempt at a Solution [/B]
105km - 105 x 10^-3m - This is wrong. It should be 1.05x 10⁵m (But I think I understand why)
57mm - 5.7 x 10^-2m
6.67x10^-11cm - 6.67x10^-12m - Wrong 6.67x10^-13m (because there are 2 zeros in 100, not one, wupps)
6x10²⁷ grams 6x10²⁴kg
9 grams per cubic centimetre - ?
100 km h^-1 -? I assume h is hour.
5 nN - ?
10μW - ?
5Gm - ?

I already know the answers, clues about how to get them for myself would be brilliant, thanks everyone.

 

[blue_leaf77]

G = giga, μ = micro, h = hour.

9 grams per cubic centimetre - ?

If I rewrite it as $\frac{9\, \textrm{g}}{1\,\textrm{cm}^3}$, will you have any idea how to convert to SI?

5 nN - ?
10μW - ?
5Gm - ?

Check this link https://en.wikipedia.org/wiki/Metric_prefix .

 

[DrClaude]

I am given some measurements and I am supposed to express them as standard SI units.

Allow me to be pedantic: that should be base SI units. Most of these are already in standard SI units.

 

[RabbitWho]

Hi guys, still lost with the fifth one. Thanks for trying to help. I guess now it has changed from a physics problem to a problem with my maths.

I can't see how 9g / 10 ⁵m can get to 9 x 10³ kg m²

Looking at the next one, 5nN... that site says n is nano. So Nano Newtons.. If nano is 10^-9 then it's 5 x 10 ⁹ m.. That's right.. Thank you!

10μW 10 microwatts.. 10^-7... wrong.. the book says 1 x 10 ^-5 W... What is the point in saying 1x? What happened to the other 0?

5Gm - 5 gigametres... 5 x 10⁹m... right, thanks.

I am still not flying with these, you don't happen to know where I could find something like them?

Allow me to be pedantic: that should be base SI units. Most of these are already in standard SI units.

I just wrote what my book said. You can email them :) saying on page 6 of Real World Physics there is an error. https://www.folens.ie/about-us/contact-us.. All those little hexagons fill me with dread, they were on 90% of my schoolbooks growing up, with a little bee in the middle. Only I remember it as a fly. A mean one!

 

[blue_leaf77]

I can't see how 9g / 10 ⁵m can get to 9 x 10³ kg m²

Please write everything correctly, there is no way meter can turn to meter square.

Looking at the next one, 5nN... that site says n is nano. So Nano Newtons.. If nano is 10^-9 then it's 5 x 10 ⁹ m.. That's right.. Thank you!

It's not 5 x 10 ⁹ m, remember you are converting the unit of force.

10μW 10 microwatts.. 10^-7... wrong.. the book says 1 x 10 ^-5 W... What is the point in saying 1x? What happened to the other 0?

$10 \mu\textrm{W} = 10 \times 10^{-6} \textrm{ W} = ?$.

 

[RabbitWho]

Sorry! A van driver cut me off and I fell off my bike trying not to crash into him today so I am studying with a nasty headache. Thank goodness for helmets though, right? Watch out for cyclists, van drivers, we are a squishy and fragile people.

5 x 10 9 m

5x10⁹N

Please write everything correctly, there is no way meter can turn to meter square.

9g / 1cm³ can get to 9 x 10³ kg m^-3

I'd have thought 9 g had to be 9 x 10^-3kg.. but we have got a ³, a multiply and a m^-3 instead

W=?.

I get that one now, thank you! :)

 

[blue_leaf77]

9g / 1cm3 can get to 9 x 103 kg m-3

I'd have thought 9 g had to be 9 x 10-3kg.. but we have got a 3, a multiply and a m-3 instead

The numerator changes from $9$ g to $9\times 10^{-3}$ kg. What's left is converting the denominator which is $1$ cm³. Think of the following, 1 cm is equivalent to 10^-2 m and moreover 1 cm³ can also be expressed as (1 cm)³. Using this relation you should be able to convert from cm³ to m³.

 

[DrClaude]

Watch out for cyclists, van drivers, we are a squishy and fragile people.

Especially fluffy rabbits

5x10⁹N

That's a strong force! Certainly not 5 nN...

 

[DrClaude]

I just wrote what my book said. You can email them :) saying on page 6 of Real World Physics there is an error. https://www.folens.ie/about-us/contact-us..

Bah, too much hassle. I only care that you and other visitors to the site know it

 

[blue_leaf77]

That's a strong force! Certainly not 5 nN...

How could I miss that?

 

[David Lewis]

10μW 10 microwatts.. 10-7... wrong.. the book says 1 x 10 -5 W... What is the point in saying 1x? What happened to the other 0?

We don't know if the 0 is a significant figure, or just a place holder.
If you use a sensitive, good quality power meter, you'd write 1.0 x 10^-5
But if you use a cheapy, imprecise meter, you write 1 x 10^-5

Customarily, we assume trailing zeroes to be place holders unless noted otherwise.

Also, in scientific notation, we put only one digit to the left of the decimal point, and then whatever number of digits is justified by the precision of your measuring instrument to the right of the decimal point.