# Expressing measurements in SI units

• RabbitWho
In summary: So 1.0 x 10-5 is really a bit more precise than 1 x 10-5. But if you write 1.00 x 10-5, you are claiming a precision that you don't really have.In summary, the conversation discusses the difficulties of converting measurements to standard SI units, such as kilometers to meters and grams to kilograms. The participants also discuss the abbreviations used in physics and how to convert units using the metric prefixes. They also touch on the topic of significant figures and precision when writing numbers in scientific notation.
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.

G = giga, μ = micro, h = hour.
RabbitWho said:
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?
RabbitWho said:
5 nN - ?
10μW - ?
5Gm - ?

RabbitWho
RabbitWho said:
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.

billy_joule
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?

DrClaude said:
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!

RabbitWho said:
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.
RabbitWho said:
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.
RabbitWho said:
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.
blue_leaf77 said:
5 x 10 9 m
5x109N
blue_leaf77 said:
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! :)

Last edited by a moderator:
RabbitWho said:
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.

RabbitWho
RabbitWho said:
Watch out for cyclists, van drivers, we are a squishy and fragile people.
Especially fluffy rabbits

RabbitWho said:
5x109N
That's a strong force! Certainly not 5 nN...

RabbitWho said:
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

RabbitWho
DrClaude said:
That's a strong force! Certainly not 5 nN...
How could I miss that?

RabbitWho said:
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.

RabbitWho

## 1. What is the purpose of expressing measurements in SI units?

The purpose of expressing measurements in SI units is to have a standardized system of measurement that is used globally. This allows for easier communication and comparison of data between scientists and countries.

## 2. What is the difference between SI units and other systems of measurement?

SI units, also known as the International System of Units, is a modern version of the metric system. It is based on seven base units, including the meter for length, kilogram for mass, and second for time. Other systems of measurement, such as the imperial system, have different base units and conversion factors.

## 3. How do you convert measurements to SI units?

To convert measurements to SI units, you can use conversion factors. For example, to convert from feet to meters, you would multiply the number of feet by 0.3048. Another method is to use a conversion calculator or reference chart.

## 4. Why is it important to use SI units in scientific experiments?

Using SI units in scientific experiments ensures consistency and accuracy in data. It also allows for easier calculations and comparisons between different experiments. Additionally, SI units are based on the decimal system, making it easier to work with and understand.

## 5. Are there any exceptions to using SI units?

While SI units are the preferred system of measurement in science, there are some exceptions. For example, in certain fields of study, such as astronomy and geology, other units may be used for convenience or historical reasons. However, conversion to SI units is often necessary for communication and comparison of data.

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