The four prefixes you need
Definition
Micrometre
A unit of length equal to one millionth of a metre, written µm, used for measuring cells and organelles.
- A prefix in front of a unit is a shorthand for multiplying that unit by a power of ten.
- Milli means 10−310^{-3}10−3, so 1 mm1\,\text{mm}1mm is one thousandth of a metre and is the unit you use for an image measured with a ruler.
- Micro means 10−610^{-6}10−6, so 1 μm1\,\mu\text{m}1μm is one millionth of a metre and is the working unit for whole cells and large organelles.
- Nano means 10−910^{-9}10−9, so 1 nm1\,\text{nm}1nm is one thousand millionth of a metre and is used for ribosomes, membranes and viruses.
- Pico means 10−1210^{-12}10−12, and at that scale you are measuring individual atoms rather than biological structures.
- Each prefix in that list is 100010001000 times smaller than the one before it.
Note
The symbol for micro is the Greek letter mu, written μ\muμ, so a micrometre is μm\mu\text{m}μm and is sometimes called a micron.
Converting between units
- Moving down one prefix step means multiplying by 100010001000, and moving up one step means dividing by 100010001000.
- 1 m=1000 mm1 mm=1000 μm1 μm=1000 nm1 nm=1000 pm1\,\text{m} = 1000\,\text{mm} \qquad 1\,\text{mm} = 1000\,\mu\text{m} \qquad 1\,\mu\text{m} = 1000\,\text{nm} \qquad 1\,\text{nm} = 1000\,\text{pm}1m=1000mm1mm=1000μm1μm=1000nm1nm=1000pm
- Going from a larger unit to a smaller one always makes the number bigger, which is a quick way to check the conversion went the right way.
- Going from millimetres straight to nanometres skips a step, so you multiply by 1000×1000=1061000 \times 1000 = 10^{6}1000×1000=106.
Hint
Write the conversion out as a separate line of working, because an examiner can award a method mark for a correct conversion even when the final answer is wrong.
Example
- A plant cell is measured as 0.045 mm0.045\,\text{mm}0.045mm long, and the question asks for the length in micrometres.
- Millimetres to micrometres is one step down, so multiply by 100010001000.
- 0.045 mm×1000=45 μm0.045\,\text{mm} \times 1000 = 45\,\mu\text{m}0.045mm×1000=45μm
- To reach nanometres, multiply by 100010001000 again to give 45 000 nm45\,000\,\text{nm}45000nm.
- The answer of 45 μm45\,\mu\text{m}45μm is a believable plant cell length, which confirms the conversion ran in the right direction.
Common Mistake
Dividing when you should multiply gives an answer one million times out, so always ask whether the number should have grown or shrunk before writing it down.
Standard form on higher tier
Definition
Standard form
A way of writing a number as a value between 1 and 10 multiplied by a power of ten.
- Calculations using standard form are printed in bold in the Edexcel specification, which means they are assessed on higher tier only.
- A number in standard form is written as a value between 111 and 101010 multiplied by a power of ten.
- 45 μm=4.5×10−5 m20 nm=2×10−8 m45\,\mu\text{m} = 4.5 \times 10^{-5}\,\text{m} \qquad 20\,\text{nm} = 2 \times 10^{-8}\,\text{m}45μm=4.5×10−5m20nm=2×10−8m
- A negative power means the number is smaller than one, and the size of the power tells you how many places the decimal point moves.
- Standard form is what makes cell sizes comparable, because 2×10−82 \times 10^{-8}2×10−8 is instantly recognisable as smaller than 4.5×10−54.5 \times 10^{-5}4.5×10−5.
Calculating in standard form
- To multiply, multiply the front numbers and add the powers.
- To divide, divide the front numbers and subtract the powers.
- An electron micrograph of a mitochondrion measures 4.5×10−2 m4.5 \times 10^{-2}\,\text{m}4.5×10−2m, and the real mitochondrion is 3×10−6 m3 \times 10^{-6}\,\text{m}3×10−6m long.
- magnification=4.5×10−23×10−6=1.5×104\text{magnification} = \dfrac{4.5 \times 10^{-2}}{3 \times 10^{-6}} = 1.5 \times 10^{4}magnification=3×10−64.5×10−2=1.5×104
- Divide 4.54.54.5 by 333 to get 1.51.51.5, then subtract the powers so that −2−(−6)=4-2 - (-6) = 4−2−(−6)=4.
- The magnification is therefore ×15 000\times 15\,000×15000, and both forms of the answer are acceptable.
Exam technique
- Use the standard form button on your calculator rather than typing out strings of zeros, since a miscounted zero is the commonest error here.
- Convert everything into metres before you start when a question mixes millimetres, micrometres and nanometres.
- Check that a front number sits between 111 and 101010, because 15×10315 \times 10^{3}15×103 is not properly in standard form.
Choosing a sensible unit
- Pick the unit that keeps the number easy to read, so a cell is quoted in micrometres rather than as 0.00002 m0.00002\,\text{m}0.00002m.
- Measure images in millimetres, quote cells and large organelles in micrometres, and quote ribosomes, membranes and viruses in nanometres.
- Keep the same unit throughout a comparison, because two sizes in different units cannot be compared directly.
- Always write the unit next to the number, since an unlabelled answer is treated as incomplete.
Self review
- State the power of ten that each of milli, micro, nano and pico stands for.
- How many nanometres are there in one micrometre?
- Convert 0.008 mm0.008\,\text{mm}0.008mm into micrometres and then into nanometres.
- Write 250 nm250\,\text{nm}250nm in metres in standard form.
- Which of these two quantities is larger, 3×10−6 m3 \times 10^{-6}\,\text{m}3×10−6m or 8×10−8 m8 \times 10^{-8}\,\text{m}8×10−8m?
