Physical science
Finance
Terminology
, Skills : introduction
SCIENTIFIC NOTATION
MULTIPLICATION x * DIVISION÷
Let's see:
W always requires one significant digit before the comma, but not zero. MULTIPLICATION 5 × 103 × 2 × 104
W Comma shift left = positive exponent (value gets bigger) =(5 × 2) × 10(3+4)
W Commas fringe to the right = negative exponent (value gets smaller)
(𝑎𝑛 )(𝑎𝑚 ) = 𝑎𝑛+𝑚 =10 × 107
ALSO CALLED THE 10TH MAGNOTATION
=1 × 108
W Express numbers as a product of 2 numbers :
3
5 × 10 ÷ 2 × 10 4
SHARING
[𝑁 × 10𝑛 ] =(5 ÷ 2) × 10(3−4)
N = number term [any number between 1 & 9,999…] (𝑎𝑛 )
n = positive / negative number =2,5 × 10−1 𝑚
= 𝑎𝑛−𝑚
(𝑎 )
=0,25
ADD + * SUBTRACT -
POWERS [OF NUMBERS]
W Step 1 :REDUCE all the numbers to the SAME power of 10
[same exponent]
W Step 2 :number terms added / subtracted (𝑎𝑛 )𝑚 = 𝑎𝑛𝑚
5 × 105 + 2 × 104 (5 × 103 )2
=50 × 104 + 2 × 104 =52 × 10(3 ×2) → raise numerical
term to indicated
= 52 × 104 = 25 × 106
power & multiply
=5,2 × 105 =2,5 × 107 exponent by indicated
power
2© Noted Summaries [Grade 10 Physical Sciences] PHYSICS www.notedsummaries.co.za
, SCIENTIFIC NOTATION
LENGTH / DISTANCES
ROOTS OF EXPONENTS Neutron or proton radius 10−15 m
Atom 10−10 m
W Step 1 :Rewrite number so that it has an even exponent Virus 10−7 m
Sheet of paper 10−4 m
W Step 2 :Find square root of number term + divide exponent
Finger width 10−2 m
by 2 (get answer) Length of football field 102 m
Height of Everest 104 m
√3,6 × 103 √5,3 × 107 Earth's circumference 107 m
Earth→Sun 1011 m
=√36 × 102 =√53 × 106 Distance to nearest star 1016 m
= √53 × 10(6÷2) Nearest galaxy 1022 m
= √36 × 10(2÷2)
Farthest visible galaxy 1026 m
= = 606 × 10 =7,3 × 103 TIME INTERVALS
Lifetime (very unstable particle) 10−23 s
Lifespan (radioactive elements) 10−22 s to s1028
Lifetime (muon) 10−6 s
Time between human heartbeats 100 s = 1 s
ON YOUR POCKET COMPUTER One day 105 s
One year 3 × 107 s
Human life 2 × 109 s
Length of recorded history 1011 s
→to type a number in scientific notation, use the [older model People on earth 1014 s
Life on earth 1017 s
calculators > ] test for numbers to the 10th power
Age of universe 1018 s
FOR EXAMPLE: COMPARATIVE MASSES
W 6 × 103 > > 6000 Electron 10−30 kg
W 3 −4
6 × 10 × 3,5 × 10 > Proton / Neutron 10−27 kg
DNA molecule 10−17 kg
> 2.1 Bacteria 10−15 kg
Mosquito 10−5 kg
Plum 10−1 kg
Person 102 kg
Ship 108 kg
Earth 6 × 10−24 kg
Sun 2 × 1030 kg
Star system 1041 kg
3© Noted Summaries [Grade 10 Physical Sciences] PHYSICS www.notedsummaries.co.za
, CONVERSION [UNITS]
SI- SYSTEM
We now need a conversion factor:
→Système International d'Unités [international system of units > measurement]
W Conversion factor > expresses the equivalence of a dimension in 2
different units 7 BASIC units:
1. Length (distance) in meters (m)
2. Time (seconds) (s)
CONVERSION SYMBOLS
3. Mass (kilogram) (kg)
tera- T 1012
giga- G 109
4. Electric current in amperes (A)
mega- m 106 5. Temperature in Kelvin (K)
kilo- k 103 = 1 000 6. Luminous intensity in candela (cd)
hecto- h 102 = 100 7. Amount of matter in moles (moles)
deca- da / D 101 = 10 AMOUNT SYMBOL SI UNIT
desi d 10−1 = 0,1 Position x meter (m)
senti c 10−2 = 0,01 Distance D meter (m)
military m 10−3 = 0,001 Displacement ∆x meter (m)
micro 𝜇 10−6 Acceleration A Meters per second squared (𝑚 ∙ 𝑠 −2)
nano a 10−9 Starting velocity 𝑣𝑖 or u Meters per second (𝑚 ∙ 𝑠 −1 )
pico p 10−12 Terminal velocity 𝑣𝑓 or f Meters per second (𝑚 ∙ 𝑠 −1 )
femto- f 10−15 Average speed f Meters per second (𝑚 ∙ 𝑠 −1 )
Mass m Kilogram (kg)
DIMENSIONAL ANALYSIS Weight w Newton (N)
Gravitational g Meters per second squared (𝑚 ∙ 𝑠 −2)
→ problem solving method that acceleration
uses the fact that any number or Potential energy 𝐸𝑝 Joule (J)
Step 1 : Write the CONVERSION
Kinetic energy 𝐸𝑘 Joule (J)
expression can be multiplied by FACTOR as a FRACTION
Height h meter (m)
one without changing its value 𝟏𝒎
Frequency f Hertz (Hz)
𝟏𝟎𝟎 𝒄𝒎 Period T Seconds (s)
→ indicate WHICH NUMBER we Step 2 : Multiply the factor by the
Wave speed f Meters per second (𝑚 ∙ 𝑠 −1 )
need to multiply / divide BV by: value to be converted
Wavelength 𝜆 meter (m)
Step 3 : Treat the units as numbers
Convert 60 cm to m (100cm = 1m) Tension Q Volts (V)
when multiplying fractions
Electric charge Q Coulomb (C)
Electric current I Amps (A)
Resistance R Ohm (Ω)
4© Noted Summaries [Grade 10 Physical Sciences] PHYSICS www.notedsummaries.co.za
Finance
Terminology
, Skills : introduction
SCIENTIFIC NOTATION
MULTIPLICATION x * DIVISION÷
Let's see:
W always requires one significant digit before the comma, but not zero. MULTIPLICATION 5 × 103 × 2 × 104
W Comma shift left = positive exponent (value gets bigger) =(5 × 2) × 10(3+4)
W Commas fringe to the right = negative exponent (value gets smaller)
(𝑎𝑛 )(𝑎𝑚 ) = 𝑎𝑛+𝑚 =10 × 107
ALSO CALLED THE 10TH MAGNOTATION
=1 × 108
W Express numbers as a product of 2 numbers :
3
5 × 10 ÷ 2 × 10 4
SHARING
[𝑁 × 10𝑛 ] =(5 ÷ 2) × 10(3−4)
N = number term [any number between 1 & 9,999…] (𝑎𝑛 )
n = positive / negative number =2,5 × 10−1 𝑚
= 𝑎𝑛−𝑚
(𝑎 )
=0,25
ADD + * SUBTRACT -
POWERS [OF NUMBERS]
W Step 1 :REDUCE all the numbers to the SAME power of 10
[same exponent]
W Step 2 :number terms added / subtracted (𝑎𝑛 )𝑚 = 𝑎𝑛𝑚
5 × 105 + 2 × 104 (5 × 103 )2
=50 × 104 + 2 × 104 =52 × 10(3 ×2) → raise numerical
term to indicated
= 52 × 104 = 25 × 106
power & multiply
=5,2 × 105 =2,5 × 107 exponent by indicated
power
2© Noted Summaries [Grade 10 Physical Sciences] PHYSICS www.notedsummaries.co.za
, SCIENTIFIC NOTATION
LENGTH / DISTANCES
ROOTS OF EXPONENTS Neutron or proton radius 10−15 m
Atom 10−10 m
W Step 1 :Rewrite number so that it has an even exponent Virus 10−7 m
Sheet of paper 10−4 m
W Step 2 :Find square root of number term + divide exponent
Finger width 10−2 m
by 2 (get answer) Length of football field 102 m
Height of Everest 104 m
√3,6 × 103 √5,3 × 107 Earth's circumference 107 m
Earth→Sun 1011 m
=√36 × 102 =√53 × 106 Distance to nearest star 1016 m
= √53 × 10(6÷2) Nearest galaxy 1022 m
= √36 × 10(2÷2)
Farthest visible galaxy 1026 m
= = 606 × 10 =7,3 × 103 TIME INTERVALS
Lifetime (very unstable particle) 10−23 s
Lifespan (radioactive elements) 10−22 s to s1028
Lifetime (muon) 10−6 s
Time between human heartbeats 100 s = 1 s
ON YOUR POCKET COMPUTER One day 105 s
One year 3 × 107 s
Human life 2 × 109 s
Length of recorded history 1011 s
→to type a number in scientific notation, use the [older model People on earth 1014 s
Life on earth 1017 s
calculators > ] test for numbers to the 10th power
Age of universe 1018 s
FOR EXAMPLE: COMPARATIVE MASSES
W 6 × 103 > > 6000 Electron 10−30 kg
W 3 −4
6 × 10 × 3,5 × 10 > Proton / Neutron 10−27 kg
DNA molecule 10−17 kg
> 2.1 Bacteria 10−15 kg
Mosquito 10−5 kg
Plum 10−1 kg
Person 102 kg
Ship 108 kg
Earth 6 × 10−24 kg
Sun 2 × 1030 kg
Star system 1041 kg
3© Noted Summaries [Grade 10 Physical Sciences] PHYSICS www.notedsummaries.co.za
, CONVERSION [UNITS]
SI- SYSTEM
We now need a conversion factor:
→Système International d'Unités [international system of units > measurement]
W Conversion factor > expresses the equivalence of a dimension in 2
different units 7 BASIC units:
1. Length (distance) in meters (m)
2. Time (seconds) (s)
CONVERSION SYMBOLS
3. Mass (kilogram) (kg)
tera- T 1012
giga- G 109
4. Electric current in amperes (A)
mega- m 106 5. Temperature in Kelvin (K)
kilo- k 103 = 1 000 6. Luminous intensity in candela (cd)
hecto- h 102 = 100 7. Amount of matter in moles (moles)
deca- da / D 101 = 10 AMOUNT SYMBOL SI UNIT
desi d 10−1 = 0,1 Position x meter (m)
senti c 10−2 = 0,01 Distance D meter (m)
military m 10−3 = 0,001 Displacement ∆x meter (m)
micro 𝜇 10−6 Acceleration A Meters per second squared (𝑚 ∙ 𝑠 −2)
nano a 10−9 Starting velocity 𝑣𝑖 or u Meters per second (𝑚 ∙ 𝑠 −1 )
pico p 10−12 Terminal velocity 𝑣𝑓 or f Meters per second (𝑚 ∙ 𝑠 −1 )
femto- f 10−15 Average speed f Meters per second (𝑚 ∙ 𝑠 −1 )
Mass m Kilogram (kg)
DIMENSIONAL ANALYSIS Weight w Newton (N)
Gravitational g Meters per second squared (𝑚 ∙ 𝑠 −2)
→ problem solving method that acceleration
uses the fact that any number or Potential energy 𝐸𝑝 Joule (J)
Step 1 : Write the CONVERSION
Kinetic energy 𝐸𝑘 Joule (J)
expression can be multiplied by FACTOR as a FRACTION
Height h meter (m)
one without changing its value 𝟏𝒎
Frequency f Hertz (Hz)
𝟏𝟎𝟎 𝒄𝒎 Period T Seconds (s)
→ indicate WHICH NUMBER we Step 2 : Multiply the factor by the
Wave speed f Meters per second (𝑚 ∙ 𝑠 −1 )
need to multiply / divide BV by: value to be converted
Wavelength 𝜆 meter (m)
Step 3 : Treat the units as numbers
Convert 60 cm to m (100cm = 1m) Tension Q Volts (V)
when multiplying fractions
Electric charge Q Coulomb (C)
Electric current I Amps (A)
Resistance R Ohm (Ω)
4© Noted Summaries [Grade 10 Physical Sciences] PHYSICS www.notedsummaries.co.za
