# 1.3 Units  (Page 4/6)

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## Using significant figures

1. Round the following numbers:
1. 123,517 $\ell$ to 2 decimal places
2. 14,328 km $·$ h ${}^{-1}$ to one decimal place
3. 0,00954 m to 3 decimal places
2. Write the following quantities in scientific notation:
1. 10130 Pa to 2 decimal places
2. 978,15 m $·$ s ${}^{-2}$ to one decimal place
3. 0,000001256 A to 3 decimal places
3. Count how many significant figures each of the quantities below has:
1. 2,590 km
2. 12,305 m $\ell$
3. 7800 kg

## Prefixes of base units

Now that you know how to write numbers in scientific notation, another important aspect of units is the prefixes that are used with the units.

Prefix

A prefix is a group of letters that are placed in front of a word. The effect of the prefix is to change meaning of the word. For example, the prefix un is often added to a word to mean not , as in un necessary which means not necessary .

In the case of units, the prefixes have a special use. The kilogram (kg) is a simple example. 1 kg is equal to 1 000 g or $1×{10}^{3}$ g. Grouping the ${10}^{3}$ and the g together we can replace the ${10}^{3}$ with the prefix k (kilo). Therefore the k takes the place of the ${10}^{3}$ . The kilogram is unique in that it is the only SI base unit containing a prefix.

In Science, all the prefixes used with units are some power of 10. [link] lists some of these prefixes. You will not use most of these prefixes, but those prefixes listed in bold should be learnt. The case of the prefix symbol is very important. Where a letter features twice in the table, it is written in uppercase for exponents bigger than one and in lowercase for exponents less than one. For example M means mega (10 ${}^{6}$ ) and m means milli (10 ${}^{-3}$ ).

 Prefix Symbol Exponent Prefix Symbol Exponent yotta Y ${10}^{24}$ yocto y ${10}^{-24}$ zetta Z ${10}^{21}$ zepto z ${10}^{-21}$ exa E ${10}^{18}$ atto a ${10}^{-18}$ peta P ${10}^{15}$ femto f ${10}^{-15}$ tera T ${10}^{12}$ pico p ${10}^{-12}$ giga G ${10}^{9}$ nano n ${10}^{-9}$ mega M ${10}^{6}$ micro $\mu$ ${10}^{-6}$ kilo k ${10}^{3}$ milli m ${10}^{-3}$ hecto h ${10}^{2}$ centi c ${10}^{-2}$ deca da ${10}^{1}$ deci d ${10}^{-1}$
There is no space and no dot between the prefix and the symbol for the unit.

Here are some examples of the use of prefixes:

• 40000 m can be written as 40 km (kilometre)
• 0,001 g is the same as $1×{10}^{-3}$ g and can be written as 1 mg (milligram)
• $2,5×{10}^{6}$ N can be written as 2,5 MN (meganewton)
• 250000 A can be written as 250 kA (kiloampere) or 0,250 MA (megaampere)
• 0,000000075 s can be written as 75 ns (nanoseconds)
• $3×{10}^{-7}$ mol can be rewritten as $0,3×{10}^{-6}$ mol, which is the same as 0,3 $\mu$ mol (micromol)

## Using scientific notation

1. Write the following in scientific notation using [link] as a reference.
1. 0,511 MV
2. 10 c $\ell$
3. 0,5 $\mu$ m
4. 250 nm
5. 0,00035 hg
2. Write the following using the prefixes in [link] .
1. 1,602 $×{10}^{-19}$ C
2. 1,992 $×{10}^{6}$ J
3. 5,98 $×{10}^{4}$ N
4. 25 $×{10}^{-4}$ A
5. 0,0075 $×{10}^{6}$ m

## The importance of units

Without units much of our work as scientists would be meaningless. We need to express our thoughts clearly and units give meaning to the numbers we measure and calculate. Depending on which units we use, the numbers are different. For example if you have 12 water, it means nothing. You could have 12 ml of water, 12 litres of water, or even 12 bottles of water. Units are an essential part of the language we use. Units must be specified when expressing physical quantities. Imagine that you are baking a cake, but the units, like grams and millilitres, for the flour, milk, sugar and baking powder are not specified!

how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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