Measurements in
Science
Part A
Contents
Introduction
Measurements in Science
Measurements
Importance of units
Reading and saying units
Using units in science
Prefixes and Measurements
Prefixes
The different prefixes
Ordering measurements
Converting to and from prefixes
Equal measurements
Converting Measurements
Converting Units
Converting Area and Volume Measurements
Converting Area Measurements
Converting Volume Measurements
Scientific Notation and Units
Using Scientific Notation
Big Numbers, Small Numbers
Names of Big and Small Numbers
Scientific Notation Number Maze
Using Big Numbers
UNIT 1: Measurements in Science
There are 4 worksheets in this unit relating to
Measurements in Science:
Volume can be affected by temperature whereas mass
will give a precise measurement.
Worksheet 1: Measurements in Science
Pounds and Newtons both measure Force.
Introduces measurement, the use of Standard (SI) units
used for measuring and symbols for abbreviation. Also
introduce the concept of base and combination units of
measurements. Some prior knowledge of units and their
symbols is assumed.
Highlight – 12500m, 65km, 22300lbs, 22300kg,
0.4536kg, 4.45Newton, $320 million
Answers to Questions.
mole = mol kilogram = kg ampere = A
second = s Kelvin = K metre = m candela = cd
symbols are used to abbreviate the measurements in a
consistent manner world wide.
Celcius = temperature hour = time millilitres = volume
second = time centimetre = length
hectare = area kilometre = length tonne = mass
litre = volume year = time megalitre = volume
gram = mass
Length = centimetre, cm. kilometre, km
Area = Acre. Hectare, ha. centimetres squared, cm2.
Temperature = Centigrade, oC. Fahrenheit, oF.
Volume = metres cubed, m3. MegaLitres, ML.
Litres, L. millilitres, mL.
Mass = grams, g. Tonne, T.
Time = hours, hr.
Acceleration = metres and seconds
Mass density = kilograms and metres
Concentration = moles and Litres
Surface tension = kilograms and seconds
Thermal cond. = kilograms, metres, seconds, Kelvin
Electrical cond.=seconds, Amperes, kilograms, metres
Luminance = candela and metres.
Ampere, candela, Kelvin, kilogram, metre, mole, second.
Worksheet 2: Importance of Units
Worksheet 3: Reading and Saying Units
Introduces the concept of superscripted number used in
measurements such as squared and cubed. Also
introduces the concept of the dash and the term per and
links this to the mathematical relationship of division
which many students are unaware of the relationship.
Answers to Questions.
m/s2 = metres per second squared
kg/m3 = kilograms per metres squared
mol/L = mole per Litre
kg/s2 = kilograms per second squared
cd/m2 = candela per metre squared
Magnetic Field Strength = A/m
Molar Volume = mol/m3
Viscosity = m2/s
Jerk = m/s3
Worksheet 4: Using Units in Science
Links the use of units to using and converting between
measurements mathematically to elaborate upon the
previous worksheet.
Answers to Questions.
100m ÷ 50s = 2 m/s
1500km ÷ 18.5hr = 81.1 km/hr
m.kg/s2 = metres x kilograms ÷ seconds squared
m2.kg/s2 = metres squared x kilograms ÷ seconds squared
m2.kg/s3 = metres squared x kilograms ÷ seconds cubed
kg/m.s2 = kilograms ÷ metres x seconds squared
Gives two interesting real life scenarios where errors in
using units have created problems.
22m ÷ 0.6s = 36.67 m/s
Answers to Questions.
22m ÷ 1000 = 0.022 km
0.6s ÷ 3600 = 0.00017hr
0.022km ÷ 0.00017hr = 132km/hr
Pounds and kilograms both measure mass
22300lbs x 0.4536 = 10115.28 kg
Pilots need to be aware of the total mass of the airplane to
ensure flight calculations are correct and to ensure plane
is not too heavy.
or
1700km ÷ 2hrs = 850 km/hr
1700000m ÷ 7200s = 236.1m/s
8km ÷ 2hr = 4km/hr
8000m ÷ 7200s = 1.11m/s
Measurements in Science
 Use the Word Bank to help complete the text below.
units
French
essential
Science
base
reporting
measured
care
Measurements are e _ _ _ _ _ _ _ _ in the study of S _ _ _ _ _ _ and c _ _ _
must be taken whenever r _ _ _ _ _ _ _ _ the measurements you make or use.
In Science, the u _ _ _ _ we use come from the "International System of
Measurements" or SI for short (abbreviated from the F _ _ _ _ _ Le Système
International d'Unités). There are seven b _ _ _ measurements from which
every other unit m _ _ _ _ _ _ _ in Science comes from. They are:
Base
Unit
Measurement of
metre
m
length
kilogram
kg
mass
second
s
time
ampere
A
electric current
Kelvin
K
temperature
mole
mol
amount of substance
candela
cd
luminous intensity

Use the table to write the
correct unit used for the
following base measurements.
mole = _____
kilogram = _____
ampere =
_____
second =
_____
Kelvin =
_____
metre =
_____
candela =
_____
 Why do you think symbols for measurements are used?
______________________________________________________________
______________________________________________________________
 Some common measurements: Write what each is measuring in the
spaces given from this list: mass, volume, time, temperature, length, area
Measuremen Measurin
t
g
Measuremen Measurin
t
g
Measuremen Measurin
t
g
Celsius
hour
millilitres
second
centimetre
hectare
kilometre
tonne
litre
year
megalitre
gram
 Measurements can have more than one unit. Write the symbol for each
unit after its name. One example has been started for you. The unit
symbols are listed here: yr, hr, m3, acre, g, cm, T, cm2, ha, ML, oC,
L, km, oF, mL
Measurement of
Length
Centimetre, cm.
Area
Temperature
Volume
Mass
Time
Units
There are many other units which are used in science that are combinations
of the base measurements.
 Complete the Table below by naming each of the base measurements
used in the following measurements. The first 3 have been done for
you. (Ignore the numbers shown at this stage)
Measurement of
area
volume
speed, velocity
acceleration
mass density
concentration
surface tension
thermal conductivity
Units used
m2
m3
m/s
m/s2
kg/m3
mol/L
kg/s2
kg·m/s3·K1
s3·A2/kg1·m3
electrical conductivity
·
luminance
cd/m2
Base Measurements Used
metres
metres
metres and seconds
 Write out the seven base measurements in alphabetical order.
Importance of Units
“On 23 July 1983, an Air Canada Boeing 767-200, halfway through its flight
from Montreal to Edmonton, ran out of fuel at altitude of 12,500m. The crew,
with no engines and only emergency power, was able to glide the aircraft
safely to a landing at Gimli Airport about 65km away.
Not enough fuel was placed into the plane in Montreal because the
technicians had put 22 300lbs (pounds) of fuel into the aircraft. They were
actually required to put 22 300kg of fuel onboard the plane.”
 Pounds and kilograms are both measurements of what? _______
 If 1 pound = 0.4536 kg, complete the following calculation to work
out exactly how many kilograms of fuel was actually put into the
plane.
22 300lbs x 0.4536 = _____________ kg
 Give one reason to explain why the mass of fuel is required as the
measurement in a plane and not the volume?
_______________________________________________________
_______________________________________________________
_______________________________________________________
“Another failure to convert measurements properly caused the loss of the
Mars Climate Orbiter, a spacecraft that smashed into the planet instead of
reaching a safe orbit. The Orbiter vanished after a rocket firing that was
supposed to put the spacecraft in orbit around Mars. An investigation
concluded that engineers failed to convert measurements of rocket thrusts
from Pounds per second to Newton per second, a metric system measuring
force. One English pound of force equals 4.45 Newton. The spacecraft was to
be a key part of the exploration of the planet. The Mars Climate Mission cost
over US $320 million.”
 Pounds and Newtons are both measurements of what? _______
 Highlight all the measurements in both of the above passages.
Reading and Saying Units
When reading or saying the units there are two things to remember:
1. Superscripted numbers are
the little numbers written
slightly above and behind the
unit symbol. A superscript 2
stands for squared. A
superscript 3 stands for cubed.
2. The Dash used is another way
of writing ‘divided by’. m/s
means metres divided by
seconds but this is normally
said as metres per second
 After reading the information above, complete the Table by
writing out the full wording for each unit given. Some have been
completed or partially completed for you
Measurement of Units used
area
m2
volume
m3
speed, velocity
m/s
acceleration
m/s2
density,
kg/m3
concentration
mol/L
surface tension
kg/s2
luminance
cd/m2
Writing or Saying Unit
metres squared
metres cubed
metres per second
Kilograms per
mole per
candela per
 Give the unit used after reading the information for each of following:
Measurement of
Magnetic Field Strength
Molar Volume
Viscosity
Jerk
Units used
Writing or Saying Unit
ampere(A) per metre
mole per metres cubed
metres squared per second
metre per seconds cubed
Using Units in Science
Units are used widely in an area like Science from measuring to calculations.
If you are observant, the units used in a measurement can tell us exactly what
mathematics needs to be performed to work out a particular calculation.
FOR EXAMPLE: If a car is travelling at 60km/hr, the units km/hr, means
kilometres divided by hours.
So, if we knew that a person walked 4 km in 2 hours we could calculate the
speed the person walked at.
HOW?
Speed is measured in km/hr, which means that 4 km ÷ by 2 hours
would give us 2 km/hr.
 Speed can also be measured in metres/seconds or m/s. If a person
walked 100 metres in 50 sec what would there speed be in m/s?
 If a car travelled 1500 km in 18.5 hours, what would be its average
speed for the journey in km/h?
Some harder units:
Force can be measured by multiplying mass times acceleration. If mass is
measured in kg and acceleration is measured in m/s2, then the units for Force
become kg.m/s2. This can be read as kg times metres divided by seconds
squared (or kilogram x metres ÷ seconds squared)
 Complete the table to show how the following units can be read.
Unit for
Newton
Joule
Watt
Pascal
Symbol
N
J
W
Pa
Units
m.kg/s2
m2.kg/s2
m2.kg/s3
kg/m.s2
Can be read as
 If a ball is thrown 22 metres in 0.6 seconds, what would be the speed
it is travelling at in m/s?
If you are really clever, you can convert between units used. If you want to
know how fast the ball is travelling in the above question in km/hr we must
first convert metres to km and seconds into hours.
Metres to kilometres = 22 metres ÷ 1000 (1000 metres in a kilometre)
=
Seconds to hours = 0.6s ÷ 3600 (60 seconds in a minute x 60 minutes in an hour)
=
 Calculate the speed of the ball in km/hr (remember km ÷ hours)
 An aeroplane travels from Brisbane to Melbourne in 2 hours. The
distance travelled is 1700km. What was its speed in km/hr and m/s?
 A student walks 8km in 2 hours. What was its speed in km/hr and
m/s?
UNIT 2: Prefixes and Measurements
There are 5 worksheets in this unit relating to prefixes
used in Measurements and units:
Worksheet 1: Prefixes and Measurements
Introduces the concept that base measurements can be
written with prefixes to simplify the number that is
written.
Answers to Questions.
Prefixes = kilo and milli
Base unit = metres
Best measurements (could be) = 150 m, 10 ha, 1ML,
100km/hr, 5 tonnes, 20.25m, 1 day, 50 m
Worksheet 2: The Different Prefixes
Introduces the different prefixes in order of size that
students are most likely to come across and asks students
to write out the wording for symbols commonly used.
Answers to Questions.
Pico, nano, milli, centi, kilo, mega, giga
km = kilometre cm = centimetre GL = gigalitre
mL = millilitre dm = decimetre nm = nanometre
pm = picometre g = microgram mg = milligram
ML = megalitre
Any 4 suitable measurements and symbols.
Worksheet 3: Ordering Measurements
Cut and Paste activity for students to order measurements
used by size and type.
Answers to Questions.
Length = pm, nm, m, mm, cm, m, km.
Area = pm2, nm2, m2, mm2, cm2, m2, km2.
Volume = pL, L, mL, L, ML, GL.
Mass = pg, ng, g, mg, g, kg.
Time = ns, s, ms, s.
Worksheet 4: Converting to and from Prefixes
Introduces the concept of converting to and from a base
unit to units with Prefixes. This could be considered the
first step in the ability to convert between any two units
given.
Answers to Questions.
5000000bytes ÷ 1000000 = 5 Mbytes
2000L ÷ 1000 = 2Litres
0.01 m ÷ 0.000001 = 10000metres
5 terabytes x 1000000000000 = 5000000000000bytes
63 megalitres x 1000000 = 63000000Litres
2300 nanometres x 0.000000001 = 0.0000023 metres
25nm x 0.000000001 = 0.000000025 m
300mg x 0.001 = 0.3 g
0.35km x 1000 = 350m
15cm x 0.01 = 0.15m
237m ÷ 1000 = 0.237km
25g ÷ 0.001 = 25000 mg
0.0878L ÷ 0.001 = 87.8ml
0.000013m ÷ 0.000001 = 13m
Prefix = giga Converting Factor = 1000000000
Prefix = mega Converting Factor = 1000000
Prefix = kilo Converting Factor = 1000
Prefix = hecto Converting Factor = 100
Prefix = deca Converting Factor = 10
Prefix = deci Converting Factor = 0.1
Prefix = centi Converting Factor = 0.01
Prefix = milli Converting Factor = 0.001
Prefix = micro Converting Factor = 0.000001
Prefix = nano Converting Factor = 0.000000001
Prefix = pico Converting Factor = 0.000000000001
Worksheet 5: Equal Measurements
Introduces the concept that numbers written with
different units can actually be of the same magnitude.
Answers to Questions.
61m = 6100cm
61mm = 6.1cm
61km = 61000m
61nm = 61000pm
61m = 0.061mm
1st Scale: 100g = 1000dg
2nd Scale: 1L = 1000mL
3rd Scale: 10m = 1000cm
4th Scale: 0.1L = 100mL
Prefixes and Measurements
 Use the Word Bank to help complete the text below.
measurement front numbers logical word prefix meaning
A p _ _ _ _ _ is a w _ _ _ that we can join in f _ _ _ _ of another word to
change its m _ _ _ _ _ _ _. In Science, prefixes are best used in front of a base
measurement in a l _ _ _ _ _ _ way to help record the m _ _ _ _ _ _ _ _ _ _
without having to write a lot of n _ _ _ _ _ _.
A road which is 257 kilometres long can also be 257,000,000 millimetres
long.
 What are the two prefixes used in the example above: ___________
 What is the base measurement used in the example above: _________
 Highlight or circle the best measurement used for each of the
following examples from the samples measurements given.
Example
Height of a
Building
Area of a
Farm
Volume of a
Lake
Speed of a Car
Mass of an
Elephant
Length of a
cricket pitch
Time for
Earth to
rotate
Width of a
hair
Sample Measurements
150 m
0.150 km
15000 cm
150000 mm
100000 m2
10 Hectares
1000000 L
1ML
100 km/hr
27.78 m/s
5000 kg
5000000 g
0.02025 km
2025cm
20250 mm
20.25 m
24hrs
1 day
1440 min
86400 sec
0.0000005
km
50µm
0.05 mm
0.0005 m
1000000000
0.10000 km2
2
cm
1000000000 219969.25
cm3
gallons
62.14
166666.7
miles/hr
cm/min
11023.1
5 tonnes
pounds
The Different Prefixes
Examples of prefixes used in measurements from biggest to smallest and
their symbols.
Name
tera giga meg kilo hect deca deci centi milli micr nano pico
aoo-
Symb
ol
T
G
M
k
h
da
d
c
m
µ
n
p
 For each of the following highlight or circle the correct answer from
the choice given.
Tera is bigger than / smaller than centi
mega is bigger than / smaller than nano
milli is bigger than / smaller than giga
pico is bigger than / smaller than micro
hecto is bigger than / smaller than kilo
centi is bigger than / smaller than kilo
deci is bigger than / smaller than deca
mega is bigger than / smaller than micro
 Use the table of prefixes to help write the names, in order from
smallest to largest, of the prefix symbols shown below:
c- G- k- M- p- m- n:
_______________________________________________________

Write out using words the following measurements. The first one has
been done for you.
measurement
km
cm
GL
mL
dm

wording
kilometre
measurement
nm
pm
µg
mg
ML
wording
Write out the words and symbols for 4 other measurements that have
prefixes that you know.
Word
Symbol
Ordering Measurements
 In the boxes below the table are many different measurements. Cut out
each and place it in the correct column in order from smallest value at
the top to biggest value at the bottom. Write the name of each unit
underneath each pasted box.
Length
Area
Volume
Mass
Time
_________________________________________
pm
kg
pL
µs
µL
pg
nm2
GL
m
pm2
µm
cm
nm
µg
ms
mm
s
µm2
mg
mL
ng
g
L
ns
km
km2
m2
ML
cm2
mm2
Converting to and from Prefixes:
To convert to and from using prefixes (in most cases) we divide or multiply
by the factor given in the following table. This however, DOES NOT work
when the units are squared or cubed as in area and volume measurements.
Prefix Symbol Converting Factor
teraT
1 000 000 000 000
gigaG
1 000 000 000
megaM 1 000 000
kilok
1 000
hectoh
100
decada 10
none) (none) 1
decid
0.1
centic
0.01
millim
0.001
microµ
0.000 001
nanon
0.000 000 001
picop
0.000 000 000 001
Converting to: (divide)
50 000 bytes of computer memory
is equal to:
50 000 ÷ 1 000 kilobytes
= 50 kilobytes
7 000 000 Litres is equal to
7 000 000 ÷ 1 000 000 megalitres
= 7 megalitres
Converting from: (multiply)
20 terabytes of computer memory is
equal to 20 x 1 000 000 000 000
bytes of memory.
= 20 000 000 000 000 bytes
6250 nanometres in length is the
same as 6250 x 0.000 000 001
metres = 0.000 00625 metres
 Read the information above and then add the prefixes to the following
Measurement Convert to
5 000 000 bytes megabytes
2 000 litres
kilolitres
0.01 metres
micrometres
Conversion
Answer
 Remove the prefixes from the following measurements
Measurement
5 terabytes
63 megalitres
2300 nanometres
Convert to
bytes
litres
metres
Conversion
Answer
 Can you convert these?
Measurement
12 ML
25 nm
300 mg
0.35 km
15 cm
237 m
25 g
0.0878 L
0.000013 m
Convert to
Litres
m
g
m
m
km
mg
ml
µm
Conversion
12 x 1000000
Answer
12000000 L
 Complete the diagram below using the correct words and conversion
factors to fill the gaps. Some have been done for you.
Symbol = G
Prefix = g _ _ _
Converting Factor
_____________
Symbol = M
Prefix = m _ _ _
Converting Factor
_____________
Symbol = k
Prefix = k _ _ _
Converting Factor
_____________
Symbol = T
Prefix = t _ _ _
Converting Factor
Symbol = h
Prefix = h _ _ _ _
Converting Factor
_____________
Symbol = da
Prefix = d _ _ _
Converting Factor
_____________
1 000 000 000 000
PREFIXES
Symbol = p
Prefix = p _ _ _ _
Converting Factor
Symbol = d
Prefix = d _ _ _
Converting Factor
_____________
0.000 000 000 001
Symbol = n
Prefix = n _ _ _
Converting Factor
_____________
Symbol = µ
Prefix = m _ _ _ _
Converting Factor
_____________
Symbol = m
Prefix = m _ _ _ _
Converting Factor
_____________
Symbol = c
Prefix = c _ _ _ _
Converting Factor
_____________
Equal Measurements
Because a measurement can be written with different units, they are still
considered the same, only the prefix changes.
For example: A 1 metre ruler is the same length as a 100cm ruler.
Match similar measurements shown below by drawing a line between them.
61 m
61 mm
61 km
61 nm
61 µm
6.1cm
61000 m
0.061 mm
6100 cm
61000 pm
 Two of the measurements below each scale are equal. Write the
correct two measurements in the scale to keep it balanced.
1) 100g 1kg 1000dg 10000mg
2) 1L 10cL 0.001dL 1000mL
3) 10m 1km 1000cm 0.01mm
4) 0.1L 10dL 100mL 1000cL
UNIT 3: Converting Measurements
There are 4 worksheets in this unit relating to
converting measurements from one prefix of a unit to
another including the conversions required for
squared and cubed units such as area and volume.
Worksheet 1: Converting Measurements
Introduces the mathematical concept for the conversion
of units from any prefix of a unit given to another prefix
for that unit.
Answers to Questions.
3 kilopascals x 10 = 30 hectopascals
5.4 centimetres x 10 = 54 millimetres
0.7 millilitres ÷ 1000 = 0.00007 Litres
650 millimetres ÷ 100 = 6.5 decimetres
12000 watts ÷ 1000 = 12 kilowatts
97000 millilitres ÷ 10000 = 9.7 decalitres
Worksheet 2: Converting Area and Volume
Measurements
Introduces the mathematical concept for the conversion
of area and volume units from any prefix of a unit given
to another prefix for that unit.
Answers to Questions.
0.01km2 x 1000000 = 10000 km2
530 mm2 ÷ 100 = 5.3cm2
2000000 ÷ 1000000 = 2km2
0.0005m3 x 1000000 = 500 cm3
30000mm3 ÷ 1000 = 30 cm3
Worksheet 3: Converting Area Measurements
Explains the mathematical concept for the conversion of
area units from any prefix of a unit given to another
prefix for that unit.
Answers to Questions.
Step 2) Number of squares = 9
Step 3) Area = 3 x 3 = 9 cm2
Step 5) Number of squares = 90
Step 6) Area = 30 x 30 = 900 m2
Step 7) 900 ÷ 9 = 100
Converting Measurements
Worksheet 4: Converting Volume Measurements
Explains the mathematical concept for the conversion of
volume units from any prefix of a unit given to another
prefix for that unit.
Answers to Questions.
Step 2) Number of smaller cubes = 8
Step 3) Volume = 2 x 2 x 2 = 8 cm3
Step 5) Volume = 20 x 20 x 20 = 8000 mm3
Step 6) Number of smaller cubes = 8000 = Volume
Step 7) 8000 ÷ 8 = 1000
In the metric system, converting from 1 prefix to the next is a simple matter
of multiplying or dividing by 10 for each step shown below taken.
Be Careful: This DOES NOT work when the units are squared or cubed as
in area and volume measurements.
When the prefixes gets smaller we multiply by 10 for each step taken.
x10
kilo-
x10
x10
hecto- deca-
x10
no
prefix
x10
deci-
x10
centi-
milli-
When the prefixes gets larger we divide by 10 for each step taken.
÷10
kilo-

÷10
hecto- deca-
÷10
÷10
no
prefix
÷10
deci-
÷10
centi-
milli-
Change the following measurements using the units given. The
first one has been done for you.
Measurement
Convert to
Conversion
Answer
2 megalitres
kilolitres
2 x 10
200kL
20 milligrams
grams
20 ÷ 10 ÷ 10 ÷ 10
0.02g
3 kilopascals
hectopascals
5.4 centimetres
millimetres
0.7 millilitres
litres
650 millimetres
decimetres
12000 watts
kilowatts
97000 millilitres
decalitres
Converting Area and Volume Measurements.
When changing units that are squared, as in measurements of area, we must
multiply or divide by 100. This is because cm2 = cm x cm, so we need to
change our units by a factor of 10 x 10 = 100 for each step taken.
x100
kilo-
x100
x100
hecto- deca-
÷100
÷100
x100
no
prefix
÷100
x100
deci-
÷100
x100
centi-
÷100
milli-
÷100
 Complete the following table.
Measurement
Convert to
Conversion
Answer
2 cm2
0.01 km2
530 mm2
2 000 000 m2
mm2
m2
cm2
km2
2 x 100
200mm2
 When changing units that are cubed, as in measurements of area, we
must multiply or divide by 1000. This is because cm3 = cm x cm x cm,
so we need to change our units by a factor of 10 x 10 x 10 = 1000 for
each step taken.
x1000 x1000 x1000
kilo-
hecto- deca-
÷1000
÷1000
no
prefix
3
Convert to
3
deci-
÷1000 ÷1000
 Complete the following table.
Measurement
x1000 x1000 x1000
2 cm
mm
3
0.0005 m
cm3
30 000 mm3
cm3
276 000 000 m3
km3
Converting Area Measurements.
centi-
÷1000
milli-
÷1000
Conversion
Answer
2 x 1000
2000mm2
Converting the units for Area measurements must be done very carefully
because the units are squared. Follow the instructions given to see why this is
the case.
Step 1: Draw a 3 cm square below with a 1 cm grid pattern.
Step 2: Count the number of squares in the grid. ________
Step 3: Calculate the area of the square in cm2: Area = Length(cm) x Width(cm)
Step 4: Draw another 3cm square below but with a 1 mm grid pattern.
Step 5: Count the number of squares in the grid. ________
Step 6: Calculate the area of the square: Area = Length(mm) x Width(mm)
Step 7: Take the value calculated in step 6 and divide by the value calculated
in step 3. This is the conversion factor for squared units.
Converting Volume Measurements.
Converting the units for Volume measurements must be
done very carefully because the units are cubed. Follow the
instructions given to see why this is the case.
Step 1: Draw a 2 cm cube below with a 1 cm grid pattern.
Step 2: Count the number of smaller cubes within the 2cm cube. ___________
Step 3: Calculate the volume of the cube in cm3:
Volume = Length(cm) x Width(cm) x Height(cm)
Step 4: Draw another 2cm cube below but with a 1mm grid pattern.
Step 5: Calculate the volume of the cube in mm3:
Volume = Length(mm) x Width(mm) x Height(mm) =
Step 6: If you could count all the smaller cubes, how many do you think there
would be? Why?
Step 7: Take the value calculated in step 5 and divide by the value calculated
in step 3. This is the conversion factor for cubed units
UNIT 4: Scientific Notation and Units
There are 5 worksheets in this unit relating to use and
understanding of Scientific Notation and the names
used for both very small and very large numbers
found in Science.
Worksheet 1: Using Scientific Notation
Introduces the concept of Scientific Notation.
Answers to Questions.
Ten Thousand– 1 x 104–1 x (10x10x10x10)
One Hundred Thousand– 1 x 105– 1 x (10x10x10x10x10)
One Million – 1 x 106 – 1 x (10x10x10x10x10x10)
Ten Million – 1 x 107 – 1 x (10x10x10x10x10x10x10)
The number of zeros in each number is the same as the
superscripted number.
One Ten Thousandth - 1 x 10-4 – 1 ÷ (10x10x10x10)
One Hundred Thousandth - 1 x 10-5
– 1 ÷ (10x10x10x10x10)
One Millionth - 1 x 10-6 – 1 ÷ (10x10x10x10x10x10)
One Ten Millionth - 1 x 10-7
– 1 ÷ (10x10x10x10x10x10x10)
Answers to Questions.
10000, 1000000, 1000000000, 1000000000000,
1000000000000000, 1000000000000000000,
1000000000000000000000,
1000000000000000000000000.
0.00001, 0.000001, 0.000000001, 0.000000000001,
0.000000000000001, 0.000000000000000001,
0.000000000000000000001,
0.000000000000000000000001
1000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000
000000000. (go on ...count them!)
Worksheet 4: Scientific Notation Number Maze
This worksheet gives students the opportunity to work
their way through a maze in order from smallest number
to biggest number given Scientific Notation.
Answers to Maze.
The number of decimal places in each number is the
same as the superscripted number.
1 x 104, 4 x 105, 5 x 106, 6 x 109
1 x 10-7, 4 x 10-4, 8 x 10-9, 7 x 10-13
Worksheet 2: Big Numbers, Small Numbers
This worksheet shows where Scientific Notation can be
found in real Science situations and uses these to have
students order numbers from biggest to smallest.
Answers to Questions.
Mass of an electron - 9.11 × 10-31 kg
Width of a hair – 50 x 10-6 m
Width of a plant cell - 1.276 x 10-5 m
Surface Area of Australia - 7,686,850 km2
Distance to the Sun – 150 000 000 km
Volume of water in the oceans – 1.3 billion km3
Time for light to cross universe – 20 x 109 years
Number of bacteria living on a human – 100 trillion
Mass of gases in the atmosphere - 5.1480×1018 kg
Number of stars in the solar system - 7 x 1022
Number of atoms in 58.5g of table salt – 6.02 x 1023
Mass of the Earth - 5.9736×1024 kg
Worksheet 3: Names of Big and Small Numbers
This worksheet gives students the names for some of the
biggest and smallest numbers that can be found and asks
students to write and name some of them.
Worksheet 5: Using Big Numbers
This worksheet gives students the opportunity to
calculate measurements equivalent to the “light year”
using things that travel slightly slower than light.
Answers to Questions.
8.17 x 1013 km.
Foot = 2.33 x 109 years
Bike = 3.73 x 108 years
Car = 1.55 x 108 years
Plane = 1.17 x 107 years
Space Shuttle = 2.33 x 105 years
To obtain the number of hours in a year.
Using Scientific Notation
Scientific Notation is simply another way of writing numbers. It is usually
used when we are dealing with very big or very small numbers.
 Complete the tables below.
Number
Words
10
100
1000
10000
100000
1000000
10000000
Ten
One Hundred
One Thousand

What this means
1 x (10)
1 x (10 x 10)
1 x (10 x 10 x 10)
How does the number of zeros in the number compare to the superscript
number in scientific notation? _____________________________
Number
Words
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
One tenth
One Hundredth
One Thousandth

Scientific
Notation
1 x 101
1 x 102
1 x 103
Scientific
Notation
1 x 10-1
1 x 10-2
1 x 10-3
What this means
1 ÷ (10)
1 ÷ (10 x 10)
1 ÷ (10 x 10 x 10)
How does the number of decimal places in the number compare to the
superscript number in scientific notation? ___________________
Number
Scientific Notation
Number
10000
0.0000001
400000
0.0004
5000000
0.000000008
6000000000
0.0000000000007
Scientific Notation
Big Numbers, Small Numbers.
Some examples of big and small numbers are given in the information
arranged below.
Distance to the Sun – 150 000 000 km
Width of a plant cell - 1.276 x 10-5 m
Surface Area of Australia - 7,686,850 km2
Time for light to cross universe – 20 x 109 years
Number of bacteria living on a human – 100 trillion
Mass of an electron - 9.11 × 10-31 kg
Number of stars in the solar system - 70 sextillion (7 x 1022)
Width of a hair – 50 x 10-6 m
Mass of gases in the atmosphere - 5.1480×1018 kg
Mass of the Earth - 5.9736×1024 kg
Number of atoms in 58.5g of table salt – 6.02 x 1023
Volume of water in the oceans – 1.3 billion km3
 Write the Numbers above out from biggest to smallest in the table
Description
Biggest
Smallest
Number
Names of Big and Small Numbers
Just about everybody knows what 100 is called: But what is 100000000000!
Scientific
Notation
Number
Name
Scientific
Notation
1 x 100
1
One
1 x 100
1
One
1 x 101
10
Ten
1 x 10-1
0.1
Tenth
1 x 102
100
Hundred
1 x 10-2
0.01
Hundredth
1 x 103
1000
Thousand
1 x 10-3
0.001
Thousandth
0.0001
Ten Thousandth
4
1 x 10
1 x 105
10000
Ten Thousand
Hundred Thousand
1 x 10
-4
Number
Name
1 x 10-5
Hundred Thousandth
1 x 106
Million
1 x 10-6
Millionth
1 x 109
Billion
1 x 10-9
Billionth
1 x 1012
Trillion
1 x 10-12
Trillionth
1 x 1015
Quadrillion
1 x 10-15
Quadrillionth
1 x 1018
Quintillion
1 x 10-18
Quintillionth
1 x 1021
Sextillion
1 x 10-21
Sextillionth
1 x 1024
Septillion
1 x 10-24
Septillionth
 Complete the table given by giving the correct name for the scientific
notation given
Scientific
Notation
3 x 103
Name
Scientific Notation
Name
6 x 10-2
7 x 1012
5 x 10-6
8 x 1018
4 x 10-9
9 x 101
6 x 10-18
24 x 1024
2 x 10-1
There is also the number Googol, which is a 1 with one hundred zeros behind
it, and the number Googolplex, which is a 1 with a Googol of zeros behind it.
 Write out a GOOGOL!!!!
Scientific Notation Number Maze
Trace a path through the number maze from start to finish moving over
increasingly bigger numbers. You may move up, down or across, but not
diagonally.
Start
3 x 10-12
5 x 10-17
3 x 109
6 x 10-14
2 x 10-18
2 x 10-23
3 x 10-17
5 x 10-17
8 x 10-17
1 x 10-15
6 x 10-14
2 x 1011
1 x 1023
1 x 109
3 x 109
4 x 109
7 x 1010
2 x 1011
9 x 1012
1 x 10-24
6 x 10-14
1 x 10-24
7 x 10-24
2 x 10-23
4 x 10-1
7 x 1010
6 x 10-18
9 x 10-18
1 x 10-17
1 x 10-24
4 x 109
2 x 10-23
3 x 10-12
3 x 10-4
1 x 10-19
5 x 108
7 x 101
9 x 10-5
2 x 1011
8 x 10-21
8 x 1013
5 x 10-17
1 x 1024
4 x 102
3 x 1018
6 x 10-23
5 x 10-17
2 x 101
2 x 10-18
8 x 106
6 x 10-14
8 x 10-10
2 x 10-21
8 x 10-21
8 x 10-10
5 x 10-17
5 x 10-9
4 x 107
8 x 106
7 x 105
6 x 104
1 x 1023
2 x 1014
9 x 10-20
3 x 109
8 x 10-10
3 x 10-12
1 x 10-22
7 x 105
1 x 1023
8 x 10-19
2 x 10-19
1 x 10-19
6 x 10-35
8 x 106
7 x 101
5 x 10-9
3 x 1018
6 x 10-14
6 x 10-23
1 x 10-22
9 x 10-20
9 x 103
7 x 10-24
3 x 1015
5 x 10-9
8 x 10-21
6 x 10-7
2 x 101
4 x 10-22
3 x 1018
2 x 1014
1 x 10-15
5 x 10-9
9 x 10-20
7 x 10-8
1 x 10-15
6 x 10-14
7 x 10-8
5 x 10-9
8 x 10-21
2 x 101
5 x 10-9
1 x 10-15
4 x 102
9 x 10-5
4 x 1016
3 x 1018
1 x 1020
2 x 10-2
4 x 109
7 x 10-22
2 x 10-21
5 x 10-21
8 x 10-21
2 x 10-20
5 x 10-20
5 x 10-21
3 x 10-4
7 x 10-24
6 x 10-7
3 x 10-6
5 x 10-6
9 x 10-5
6 x 10-14
1 x 10-24
7 x 101
2 x 10-23
1 x 10-19
5 x 10-21
1 x 1023
1 x 10-15
2 x 10-23
1 x 10-24
2 x 10-2
4 x 102
8 x 106
5 x 10-17
1 x 10-4
2 x 1014
1 x 1023
3 x 109
7 x 10-24
2 x 1014
1 x 1020
1 x 10-4
5 x 10-17
2 x 10-23
2 x 101
6 x 10-18
7 x 1010
8 x 10-21
1 x 1024
4 x 102
8 x 10-10
2 x 10-18
7 x 101
8 x 1013
6 x 10-23
1 x 10-4
3 x 10-6
4 x 10-1
6 x 10-14
2 x 10-23
8 x 106
1 x 1029
8 x 10-21
3 x 10-4
2 x 10-2
4 x 10-1
1 x 100
8 x 10-21
9 x 10-5
7 x 1015
Finish
 Highlight each of the following on the maze and write the answer in
the space given.
 What is the smallest number found on the maze? ______________
 What is the largest number found on the maze? ______________
 What number is the same as one? ______________
Using Big Numbers
In Science Fiction, spaceships cross the galaxy in minutes, and space travel to
distant stars seems like a reasonable option. Sirius is the brightest star in the
night sky and is a relatively close star, but its distance from Earth is still 8.6
light years. What is a "light year"?
The distance that light travels in one year is called a light-year and is about
9.5 trillion kilometers! Note that "Light Years" are distance measurements,
not time measurements.
 Calculate the distance to Sirius in km. (8.6 x 9.5 trillion km)
So how long would it take to travel to Sirius? Obviously this depends upon
the speed we are moving at.
OBVIOUSLY some of these are IMPOSSIBLE - but if we were travelling in
the following ways, how long would it take each to get to Sirius? The first
calculation has been partly done to assist you with the calculations required.
Travel By:
Speed
Distance travelled in one year
Time to get to Sirius
= km to Sirius ÷ 35040km/yr
Foot
4 km/h
Bike
25 km/h
Car
60 km/h
Plane
800 km/h
Space
Shuttle
40,000
km/h
4 x 24 x 365 = 35040km/yr = _________________ years
 Why was it necessary to multiply by 24 and then 365 in the above
calculations? ________________________________________
_______________________________________________________
_______________________________________________________