1.1.1 SI units for physical quantities

Physical quantities and SI units

Definition

Physical quantity

A physical quantity is a property of an object or system that can be measured, and is written as a number together with a unit.

Definition

SI unit

An SI unit is the internationally agreed unit used to measure a physical quantity, such as the metre, kilogram or second.

SI stands for the International System of Units, which gives scientists a common measurement language.
A complete measurement needs both a number and a unit, so $12$ is incomplete but $N12\ \text{N}$ states a force.
Base units are defined independently, while derived units are formed by multiplying or dividing other units according to an equation.
At GCSE, the most important SI base units are the metre $m\text{m}$ , kilogram $kg\text{kg}$ , second $s\text{s}$ , ampere $A\text{A}$ and kelvin $K\text{K}$ .

Units for motion and waves

Length, distance, displacement, height, extension and wavelength use the metre, $m\text{m}$ .
Area uses square metres, $m2\text{m}^{2}$ , because two lengths are multiplied.
Volume uses cubic metres, $m3\text{m}^{3}$ , because three lengths are multiplied.
Mass uses the kilogram, $kg\text{kg}$ , and must not be confused with weight.
Time and wave period use the second, $s\text{s}$ .
Speed and velocity use metres per second, $m/s\text{m/s}$ .
Acceleration uses metres per second squared, $m/s2\text{m/s}^{2}$ .
Density uses kilograms per cubic metre, $kg/m3\text{kg/m}^{3}$ .
Frequency uses the hertz, $Hz\text{Hz}$ , where $s−11\ \text{Hz}=1\ \text{s}^{-1}$ .
Angles use degrees, $∘^{\circ}$ .

Units for forces and energy

Force, weight, upthrust and resultant force use the newton, $N\text{N}$ .
Gravitational field strength uses newtons per kilogram, $N/kg\text{N/kg}$ .
Spring constant uses newtons per metre, $N/m\text{N/m}$ .
Energy transferred and work done use the joule, $J\text{J}$ .
Power uses the watt, $W\text{W}$ , with $J/s1\ \text{W}=1\ \text{J/s}$ .
Moment of a force uses the newton metre, $m\text{N m}$ .
Pressure uses the pascal, $Pa\text{Pa}$ , where $N/m21\ \text{Pa}=1\ \text{N/m}^{2}$ .
Momentum uses kilogram metres per second, $m/s\text{kg m/s}$ .

Units for electricity and radiation

Electric current uses the ampere, $A\text{A}$ .
Potential difference uses the volt, $V\text{V}$ , where $J/C1\ \text{V}=1\ \text{J/C}$ .
Resistance uses the ohm, $Ω\Omega$ .
Electric charge uses the coulomb, $C\text{C}$ .
Magnetic flux density uses the tesla, $T\text{T}$ .
Radioactive activity uses the becquerel, $Bq\text{Bq}$ , where $Bq1\ \text{Bq}$ means one nuclear decay per second.

Units for thermal physics

Temperature uses degrees Celsius, $∘C^{\circ}\text{C}$ , or kelvin, $K\text{K}$ , according to the equation and data.
Specific heat capacity uses joules per kilogram per degree Celsius, $∘C)\text{J/(kg}\,^{\circ}\text{C)}$ .
Specific latent heat uses joules per kilogram, $J/kg\text{J/kg}$ .
Efficiency has no unit because it is a ratio of two quantities with the same unit, and it may be written as a decimal or percentage.

Example

A spring has force $NF=12\ \text{N}$ and extension $mx=0.080\ \text{m}$ , with $F = k x$ .
Rearrange the equation to $k=Fxk=\dfrac{F}{x}$ .
Substitute to give $mk=\dfrac{12\ \text{N}}{0.080\ \text{m}}$ .
Evaluate to obtain $N/mk=150\ \text{N/m}$ , because newtons are divided by metres.

Writing units accurately

Unit symbols named after people use capital letters, including $N\text{N}$ , $J\text{J}$ , $W\text{W}$ , $A\text{A}$ , $V\text{V}$ , $Hz\text{Hz}$ , $Pa\text{Pa}$ , $C\text{C}$ , $T\text{T}$ and $Bq\text{Bq}$ .
Written unit names use lower-case letters, including newton, joule and watt.
Unit symbols do not take a plural ending, so five newtons is written $N5\ \text{N}$ .

Common Mistake

Do not give mass in newtons or weight in kilograms, because mass and weight are different physical quantities.
Do not interchange energy in joules with power in watts.
Do not confuse a moment in $m\text{N m}$ with momentum in $m/s\text{kg m/s}$ .
Do not omit squared or cubed powers from $m2\text{m}^{2}$ , $m3\text{m}^{3}$ , $m/s2\text{m/s}^{2}$ or $kg/m3\text{kg/m}^{3}$ .

Exam technique

Write the requested unit beside every final numerical answer unless the answer line already supplies it.
Use the resulting unit to check the equation, because an acceleration result in $m/s\text{m/s}$ shows that the calculation is incomplete or incorrect.
Keep the unit visible during substitution when it helps distinguish quantities such as mass, weight, energy and power.

Self review

What two parts make a complete measurement?
Which units measure force, energy and power?
How can a derived unit be reconstructed from an equation?
Why does efficiency have no unit?

1.1.2 Unit prefixes, conversions, significant figures and standard form

Unit prefixes

Definition

Unit prefix

A unit prefix is a symbol placed before a unit to show that the unit has been multiplied by a power of ten, such as kilo for one thousand or milli for one thousandth.

Giga, symbol $G\text{G}$ , means $×109\times 10^{9}$ , so $W1\ \text{GW}=1\times10^{9}\ \text{W}$ .
Mega, symbol $M\text{M}$ , means $×106\times 10^{6}$ , so $J1\ \text{MJ}=1\times10^{6}\ \text{J}$ .
Kilo, symbol $k\text{k}$ , means $×103\times 10^{3}$ , so $m1\ \text{km}=1\times10^{3}\ \text{m}$ .
Centi, symbol $c\text{c}$ , means $×10−2\times 10^{-2}$ , so $m1\ \text{cm}=1\times10^{-2}\ \text{m}$ .
Milli, symbol $m\text{m}$ , means $×10−3\times 10^{-3}$ , so $A1\ \text{mA}=1\times10^{-3}\ \text{A}$ .
Micro, symbol $μ\mu$ , means $×10−6\times 10^{-6}$ , so $C1\ \mu\text{C}=1\times10^{-6}\ \text{C}$ .
Nano, symbol $n\text{n}$ , means $×10−9\times 10^{-9}$ , so $m1\ \text{nm}=1\times10^{-9}\ \text{m}$ .
To remove a prefix, multiply the numerical value by the prefix factor, and to introduce a prefix, divide by that factor.

Example

A current of $mA850\ \text{mA}$ is converted using milli $10^{-3}$ .
$A850\ \text{mA}=850\times10^{-3}\ \text{A}=0.850\ \text{A}$ .
A power of $W2.4\times10^{6}\ \text{W}$ is converted using mega $10^{6}$ .
$MW2.4\times10^{6}\ \text{W}=2.4\ \text{MW}$ .

Converting units

Definition

Unit conversion

A unit conversion changes the unit used to express a quantity without changing the physical quantity itself.

Convert values to the units required by the equation before substitution, because a correct equation with inconsistent units gives an incorrect number.
$s1\ \text{minute}=60\ \text{s}$ and $s1\ \text{hour}=3600\ \text{s}$ .
Convert hours to seconds by multiplying by $3600$ , and convert seconds to hours by dividing by $3600$ .
$mm1\ \text{m}=100\ \text{cm}=1000\ \text{mm}$ .
$g1\ \text{kg}=1000\ \text{g}$ , so grams are converted to kilograms by dividing by $1000$ .
Converting to a smaller unit gives a larger numerical value, while converting to a larger unit gives a smaller numerical value.

Converting compound units

A compound unit contains more than one unit, so every part of the unit must be converted.
For speed, $m/s1\ \text{km/h}=\dfrac{1000\ \text{m}}{3600\ \text{s}}=\dfrac{1}{3.6}\ \text{m/s}$ .
Convert kilometres per hour to metres per second by dividing by $3.6$ , and convert metres per second to kilometres per hour by multiplying by $3.6$ .
For squared and cubed units, the conversion factor must also be squared or cubed, so $m21\ \text{cm}^{2}=(10^{-2}\ \text{m})^{2}=10^{-4}\ \text{m}^{2}$ .
Likewise, $m31\ \text{cm}^{3}=(10^{-2}\ \text{m})^{3}=10^{-6}\ \text{m}^{3}$ .

Example

A journey time of $h1.75\ \text{h}$ is converted by multiplying by $3600$ .
$st=1.75\times3600=6300\ \text{s}$ .
A speed of $km/h126\ \text{km/h}$ is converted by dividing by $3.6$ .
$m/sv=126\div3.6=35.0\ \text{m/s}$ .

Standard form

Definition

Standard form

Standard form writes a number as A multiplied by ten to the power n, where A is between 1 and 10 and n is an integer.

Move the decimal point until exactly one non-zero digit remains before it, then use the number of places moved as the magnitude of the power.
A large number has a positive power, such as $000=6.5×1066\,500\,000=6.5\times10^{6}$ .
A number between zero and one has a negative power, such as $45=4.5×10−70.000\,000\,45=4.5\times10^{-7}$ .
When multiplying standard-form values, multiply the leading numbers and add the powers, then rewrite the result so the leading number lies between $1$ and $10$ .
When dividing standard-form values, divide the leading numbers and subtract the powers, then normalise the result.

Example

$(3.0×108)(2.0×10−6)=(3.0×2.0)×108−6(3.0\times10^{8})(2.0\times10^{-6})=(3.0\times2.0)\times10^{8-6}$ .
The result is $6.0×1026.0\times10^{2}$ .
$8.4×1072.0×103=8.42.0×107−3\dfrac{8.4\times10^{7}}{2.0\times10^{3}}=\dfrac{8.4}{2.0}\times10^{7-3}$ .
The result is $4.2×1044.2\times10^{4}$ .

Significant figures

Definition

Significant figures

Significant figures are the digits in a number that show its measured precision, starting from the first non-zero digit.

All non-zero digits are significant, and zeros between significant digits are also significant.
Zeros before the first non-zero digit are not significant, so $0.00456$ has three significant figures.
Trailing zeros after a decimal point are significant, so $2.50$ has three significant figures.
To round to a stated number of significant figures, keep the required digits and inspect the next digit.
If the next digit is $5$ or more, increase the last retained digit by one, and if it is below $5$ , leave the last retained digit unchanged.
Keep unrounded calculator values during working and round only the final answer.

Example

The value $0.007864$ rounded to three significant figures keeps $7$ , $8$ and $6$ .
The next digit is $4$ , so the rounded value is $0.00786$ .
The value $74658\,746$ rounded to three significant figures keeps $5$ , $8$ and $7$ .
The next digit is $4$ , so the rounded value is $70058\,700$ , or $5.87×1045.87\times10^{4}$ .

Example

A train moves at $km/h126\ \text{km/h}$ for $min1\ \text{h}\ 45\ \text{min}$ .
Convert the speed: $m/s126\div3.6=35.0\ \text{m/s}$ .
Convert the time: $s(1\times3600)+(45\times60)=6300\ \text{s}$ .
Use $d = v t$ to obtain $md=35.0\times6300=220\,500\ \text{m}$ .
Write the result in standard form and round to three significant figures: $md=2.21\times10^{5}\ \text{m}$ .

Common Mistake

Do not confuse lower-case $m\text{m}$ for milli with upper-case $M\text{M}$ for mega.
Do not treat significant figures as decimal places, because $0.00456$ to two significant figures is $0.0046$ .
Do not convert $cm2\text{cm}^{2}$ or $cm3\text{cm}^{3}$ using only the linear factor.
Do not round intermediate calculator values, because early rounding can change the final answer.

Exam technique

Write each conversion on a separate line before substitution so that the method remains clear if later arithmetic is incorrect.
Check the requested output unit before calculating, because the final conversion may carry a separate mark.
Give the answer to the stated number of significant figures, or use the precision of the supplied data when the question asks for an appropriate value.
Include the final unit and use the expected size of the answer as a conversion check.

Self review

What powers of ten correspond to giga, mega, kilo, centi, milli, micro and nano?
How are kilometres per hour converted to metres per second?
What conditions must $A$ and $n$ satisfy in standard form?
Which zeros count as significant figures?
Why should rounding be left until the final line?

1.1.1 SI units for physical quantities

Physical quantities and SI units

Definition

Physical quantity

A physical quantity is a property of an object or system that can be measured, and is written as a number together with a unit.

Definition

SI unit

An SI unit is the internationally agreed unit used to measure a physical quantity, such as the metre, kilogram or second.

SI stands for the International System of Units, which gives scientists a common measurement language.
A complete measurement needs both a number and a unit, so $12$ is incomplete but $N12\ \text{N}$ states a force.
Base units are defined independently, while derived units are formed by multiplying or dividing other units according to an equation.
At GCSE, the most important SI base units are the metre $m\text{m}$ , kilogram $kg\text{kg}$ , second $s\text{s}$ , ampere $A\text{A}$ and kelvin $K\text{K}$ .

Units for motion and waves

Length, distance, displacement, height, extension and wavelength use the metre, $m\text{m}$ .
Area uses square metres, $m2\text{m}^{2}$ , because two lengths are multiplied.
Volume uses cubic metres, $m3\text{m}^{3}$ , because three lengths are multiplied.
Mass uses the kilogram, $kg\text{kg}$ , and must not be confused with weight.
Time and wave period use the second, $s\text{s}$ .
Speed and velocity use metres per second, $m/s\text{m/s}$ .
Acceleration uses metres per second squared, $m/s2\text{m/s}^{2}$ .
Density uses kilograms per cubic metre, $kg/m3\text{kg/m}^{3}$ .
Frequency uses the hertz, $Hz\text{Hz}$ , where $s−11\ \text{Hz}=1\ \text{s}^{-1}$ .
Angles use degrees, $∘^{\circ}$ .

Units for forces and energy

Force, weight, upthrust and resultant force use the newton, $N\text{N}$ .
Gravitational field strength uses newtons per kilogram, $N/kg\text{N/kg}$ .
Spring constant uses newtons per metre, $N/m\text{N/m}$ .
Energy transferred and work done use the joule, $J\text{J}$ .
Power uses the watt, $W\text{W}$ , with $J/s1\ \text{W}=1\ \text{J/s}$ .
Moment of a force uses the newton metre, $m\text{N m}$ .
Pressure uses the pascal, $Pa\text{Pa}$ , where $N/m21\ \text{Pa}=1\ \text{N/m}^{2}$ .
Momentum uses kilogram metres per second, $m/s\text{kg m/s}$ .

Units for electricity and radiation

Electric current uses the ampere, $A\text{A}$ .
Potential difference uses the volt, $V\text{V}$ , where $J/C1\ \text{V}=1\ \text{J/C}$ .
Resistance uses the ohm, $Ω\Omega$ .
Electric charge uses the coulomb, $C\text{C}$ .
Magnetic flux density uses the tesla, $T\text{T}$ .
Radioactive activity uses the becquerel, $Bq\text{Bq}$ , where $Bq1\ \text{Bq}$ means one nuclear decay per second.

Units for thermal physics

Temperature uses degrees Celsius, $∘C^{\circ}\text{C}$ , or kelvin, $K\text{K}$ , according to the equation and data.
Specific heat capacity uses joules per kilogram per degree Celsius, $∘C)\text{J/(kg}\,^{\circ}\text{C)}$ .
Specific latent heat uses joules per kilogram, $J/kg\text{J/kg}$ .
Efficiency has no unit because it is a ratio of two quantities with the same unit, and it may be written as a decimal or percentage.

Example

A spring has force $NF=12\ \text{N}$ and extension $mx=0.080\ \text{m}$ , with $F = k x$ .
Rearrange the equation to $k=Fxk=\dfrac{F}{x}$ .
Substitute to give $mk=\dfrac{12\ \text{N}}{0.080\ \text{m}}$ .
Evaluate to obtain $N/mk=150\ \text{N/m}$ , because newtons are divided by metres.

Writing units accurately

Unit symbols named after people use capital letters, including $N\text{N}$ , $J\text{J}$ , $W\text{W}$ , $A\text{A}$ , $V\text{V}$ , $Hz\text{Hz}$ , $Pa\text{Pa}$ , $C\text{C}$ , $T\text{T}$ and $Bq\text{Bq}$ .
Written unit names use lower-case letters, including newton, joule and watt.
Unit symbols do not take a plural ending, so five newtons is written $N5\ \text{N}$ .

Common Mistake

Do not give mass in newtons or weight in kilograms, because mass and weight are different physical quantities.
Do not interchange energy in joules with power in watts.
Do not confuse a moment in $m\text{N m}$ with momentum in $m/s\text{kg m/s}$ .
Do not omit squared or cubed powers from $m2\text{m}^{2}$ , $m3\text{m}^{3}$ , $m/s2\text{m/s}^{2}$ or $kg/m3\text{kg/m}^{3}$ .

Exam technique

Write the requested unit beside every final numerical answer unless the answer line already supplies it.
Use the resulting unit to check the equation, because an acceleration result in $m/s\text{m/s}$ shows that the calculation is incomplete or incorrect.
Keep the unit visible during substitution when it helps distinguish quantities such as mass, weight, energy and power.

Self review

What two parts make a complete measurement?
Which units measure force, energy and power?
How can a derived unit be reconstructed from an equation?
Why does efficiency have no unit?

1.1.2 Unit prefixes, conversions, significant figures and standard form

Unit prefixes

Definition

Unit prefix

A unit prefix is a symbol placed before a unit to show that the unit has been multiplied by a power of ten, such as kilo for one thousand or milli for one thousandth.

Giga, symbol $G\text{G}$ , means $×109\times 10^{9}$ , so $W1\ \text{GW}=1\times10^{9}\ \text{W}$ .
Mega, symbol $M\text{M}$ , means $×106\times 10^{6}$ , so $J1\ \text{MJ}=1\times10^{6}\ \text{J}$ .
Kilo, symbol $k\text{k}$ , means $×103\times 10^{3}$ , so $m1\ \text{km}=1\times10^{3}\ \text{m}$ .
Centi, symbol $c\text{c}$ , means $×10−2\times 10^{-2}$ , so $m1\ \text{cm}=1\times10^{-2}\ \text{m}$ .
Milli, symbol $m\text{m}$ , means $×10−3\times 10^{-3}$ , so $A1\ \text{mA}=1\times10^{-3}\ \text{A}$ .
Micro, symbol $μ\mu$ , means $×10−6\times 10^{-6}$ , so $C1\ \mu\text{C}=1\times10^{-6}\ \text{C}$ .
Nano, symbol $n\text{n}$ , means $×10−9\times 10^{-9}$ , so $m1\ \text{nm}=1\times10^{-9}\ \text{m}$ .
To remove a prefix, multiply the numerical value by the prefix factor, and to introduce a prefix, divide by that factor.

Example

A current of $mA850\ \text{mA}$ is converted using milli $10^{-3}$ .
$A850\ \text{mA}=850\times10^{-3}\ \text{A}=0.850\ \text{A}$ .
A power of $W2.4\times10^{6}\ \text{W}$ is converted using mega $10^{6}$ .
$MW2.4\times10^{6}\ \text{W}=2.4\ \text{MW}$ .

Converting units

Definition

Unit conversion

A unit conversion changes the unit used to express a quantity without changing the physical quantity itself.

Convert values to the units required by the equation before substitution, because a correct equation with inconsistent units gives an incorrect number.
$s1\ \text{minute}=60\ \text{s}$ and $s1\ \text{hour}=3600\ \text{s}$ .
Convert hours to seconds by multiplying by $3600$ , and convert seconds to hours by dividing by $3600$ .
$mm1\ \text{m}=100\ \text{cm}=1000\ \text{mm}$ .
$g1\ \text{kg}=1000\ \text{g}$ , so grams are converted to kilograms by dividing by $1000$ .
Converting to a smaller unit gives a larger numerical value, while converting to a larger unit gives a smaller numerical value.

Converting compound units

A compound unit contains more than one unit, so every part of the unit must be converted.
For speed, $m/s1\ \text{km/h}=\dfrac{1000\ \text{m}}{3600\ \text{s}}=\dfrac{1}{3.6}\ \text{m/s}$ .
Convert kilometres per hour to metres per second by dividing by $3.6$ , and convert metres per second to kilometres per hour by multiplying by $3.6$ .
For squared and cubed units, the conversion factor must also be squared or cubed, so $m21\ \text{cm}^{2}=(10^{-2}\ \text{m})^{2}=10^{-4}\ \text{m}^{2}$ .
Likewise, $m31\ \text{cm}^{3}=(10^{-2}\ \text{m})^{3}=10^{-6}\ \text{m}^{3}$ .

Example

A journey time of $h1.75\ \text{h}$ is converted by multiplying by $3600$ .
$st=1.75\times3600=6300\ \text{s}$ .
A speed of $km/h126\ \text{km/h}$ is converted by dividing by $3.6$ .
$m/sv=126\div3.6=35.0\ \text{m/s}$ .

Standard form

Definition

Standard form

Standard form writes a number as A multiplied by ten to the power n, where A is between 1 and 10 and n is an integer.

Move the decimal point until exactly one non-zero digit remains before it, then use the number of places moved as the magnitude of the power.
A large number has a positive power, such as $000=6.5×1066\,500\,000=6.5\times10^{6}$ .
A number between zero and one has a negative power, such as $45=4.5×10−70.000\,000\,45=4.5\times10^{-7}$ .
When multiplying standard-form values, multiply the leading numbers and add the powers, then rewrite the result so the leading number lies between $1$ and $10$ .
When dividing standard-form values, divide the leading numbers and subtract the powers, then normalise the result.

Example

$(3.0×108)(2.0×10−6)=(3.0×2.0)×108−6(3.0\times10^{8})(2.0\times10^{-6})=(3.0\times2.0)\times10^{8-6}$ .
The result is $6.0×1026.0\times10^{2}$ .
$8.4×1072.0×103=8.42.0×107−3\dfrac{8.4\times10^{7}}{2.0\times10^{3}}=\dfrac{8.4}{2.0}\times10^{7-3}$ .
The result is $4.2×1044.2\times10^{4}$ .

Significant figures

Definition

Significant figures

Significant figures are the digits in a number that show its measured precision, starting from the first non-zero digit.

All non-zero digits are significant, and zeros between significant digits are also significant.
Zeros before the first non-zero digit are not significant, so $0.00456$ has three significant figures.
Trailing zeros after a decimal point are significant, so $2.50$ has three significant figures.
To round to a stated number of significant figures, keep the required digits and inspect the next digit.
If the next digit is $5$ or more, increase the last retained digit by one, and if it is below $5$ , leave the last retained digit unchanged.
Keep unrounded calculator values during working and round only the final answer.

Example

The value $0.007864$ rounded to three significant figures keeps $7$ , $8$ and $6$ .
The next digit is $4$ , so the rounded value is $0.00786$ .
The value $74658\,746$ rounded to three significant figures keeps $5$ , $8$ and $7$ .
The next digit is $4$ , so the rounded value is $70058\,700$ , or $5.87×1045.87\times10^{4}$ .

Example

A train moves at $km/h126\ \text{km/h}$ for $min1\ \text{h}\ 45\ \text{min}$ .
Convert the speed: $m/s126\div3.6=35.0\ \text{m/s}$ .
Convert the time: $s(1\times3600)+(45\times60)=6300\ \text{s}$ .
Use $d = v t$ to obtain $md=35.0\times6300=220\,500\ \text{m}$ .
Write the result in standard form and round to three significant figures: $md=2.21\times10^{5}\ \text{m}$ .

Common Mistake

Do not confuse lower-case $m\text{m}$ for milli with upper-case $M\text{M}$ for mega.
Do not treat significant figures as decimal places, because $0.00456$ to two significant figures is $0.0046$ .
Do not convert $cm2\text{cm}^{2}$ or $cm3\text{cm}^{3}$ using only the linear factor.
Do not round intermediate calculator values, because early rounding can change the final answer.

Exam technique

Write each conversion on a separate line before substitution so that the method remains clear if later arithmetic is incorrect.
Check the requested output unit before calculating, because the final conversion may carry a separate mark.
Give the answer to the stated number of significant figures, or use the precision of the supplied data when the question asks for an appropriate value.
Include the final unit and use the expected size of the answer as a conversion check.

Self review

What powers of ten correspond to giga, mega, kilo, centi, milli, micro and nano?
How are kilometres per hour converted to metres per second?
What conditions must $A$ and $n$ satisfy in standard form?
Which zeros count as significant figures?
Why should rounding be left until the final line?

1.1 Units and quantities

1.1.1 SI units for physical quantities

Physical quantities and SI units

Units for motion and waves

Units for forces and energy

Units for electricity and radiation

Units for thermal physics

Writing units accurately

1.1.2 Unit prefixes, conversions, significant figures and standard form

Unit prefixes

Converting units

Converting compound units

Standard form

Significant figures

Recap questions

Review 1.1 Units and quantities by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Remember key concepts with flashcards

1.1 Units and quantities

1.1.1 SI units for physical quantities

Physical quantities and SI units

Units for motion and waves

Units for forces and energy

Units for electricity and radiation

Units for thermal physics

Writing units accurately

1.1.2 Unit prefixes, conversions, significant figures and standard form

Unit prefixes

Converting units

Converting compound units

Standard form

Significant figures

Recap questions

Review 1.1 Units and quantities by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Remember key concepts with flashcards

1.1 Units and quantities

1.1.1 SI units for physical quantities

Physical quantities and SI units

Units for motion and waves

Units for forces and energy

Units for electricity and radiation

Units for thermal physics

Writing units accurately

1.1.2 Unit prefixes, conversions, significant figures and standard form

Unit prefixes

Converting units

Converting compound units

Standard form

Significant figures

Recap questions

Review 1.1 Units and quantities by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Remember key concepts with flashcards

1.1 Units and quantities Revision Guide

1.1 Units and quantities

1.1.1 SI units for physical quantities

Physical quantities and SI units

Units for motion and waves

Units for forces and energy

Units for electricity and radiation

Units for thermal physics

Writing units accurately

1.1.2 Unit prefixes, conversions, significant figures and standard form

Unit prefixes

Converting units

Converting compound units

Standard form

Significant figures

Recap questions

Review 1.1 Units and quantities by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Remember key concepts with flashcards

1.1 Units and quantities Revision Guide