# Expressing measurements in SI units

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1. Aug 22, 2016

### RabbitWho

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
3. The attempt at a solution

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.

2. Aug 22, 2016

### blue_leaf77

G = giga, μ = micro, h = hour.
If I rewrite it as $\frac{9\, \textrm{g}}{1\,\textrm{cm}^3}$, will you have any idea how to convert to SI?
Check this link https://en.wikipedia.org/wiki/Metric_prefix .

3. Aug 22, 2016

### Staff: Mentor

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

4. Aug 23, 2016

### 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?

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!

5. Aug 23, 2016

### blue_leaf77

Please write everything correctly, there is no way meter can turn to meter square.
It's not 5 x 10 9 m, remember you are converting the unit of force.
$10 \mu\textrm{W} = 10 \times 10^{-6} \textrm{ W} = ?$.

6. Aug 23, 2016

### 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.

5x109N

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

I get that one now, thank you! :)

Last edited by a moderator: Aug 23, 2016
7. Aug 23, 2016

### blue_leaf77

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.

8. Aug 23, 2016

### Staff: Mentor

Especially fluffy rabbits

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

9. Aug 23, 2016

### Staff: Mentor

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

10. Aug 23, 2016

### blue_leaf77

How could I miss that?

11. Aug 23, 2016

### David Lewis

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.