Prefix (Metric) Notation Notes for the Instructor
Word notation – Three hundred million
Normal notation – 300,000,000
Scientific notation – 3 x 108
Engineering notation - 300 x 106
Prefix (Metric notation – 300 M
Alternate notations - 0.3 x 109 300,000 x 103
What is the function of each notation?
Word notation is how we write out the quantity using words. This is how we
write quantities on a check.
Normal notation is just the whole magnitude of the number. Sometimes the
number is easy to manipulate and sometimes it is difficult, especially when the
number is less than one.
Scientific notation is a way to express a number as a number, one or greater
but less than 10 times 10 raised to a power, such that the magnitude is
expressed as an exponent. Scientific notation makes handling big or small
numbers easily. If you express your numbers in scientific notation, then answers
to calculations can be estimated easily.
Quantities: Easy to say, write, and manipulate. Easy to punch into a calculator.
But the real reasons have to do with slide rulers and logarithms.
Engineering notation – What is it? Can you figure it out? Let’s try another one:
Normal notation: 0.000 000 020
Scientific notation: 2.0 x 10-8
Engineering notation: 20. X 10-9
Metric notation: 20 n
Engineering notation is the quantity expressed as a number between 1 and
1000 times 10 raised to a power divisible by 3.
Prefix (metric) notation: This is when you take your engineering notation and
substitute a prefix for the power of 10. See chart for appropriate prefixes.
I changed mole day: A mole is a metric base unit 6.02 x 1023, or better yet, 602
x 1021 or better yet: 602 Z Mole Day is now October 21 instead of October 23.
When doing calculations in science: Teach your students the meaning of
prefixes. Instead of doing dimensional analysis on your prefixes, just substitute
in the number for the prefix:
Good example: A particular wavelength of visible light is 750 nm. Calculate the
frequency of the light in Hz.  = c/
 = 3 x 108 m s-1
750 x 10-9 m now the student can see the units of s-1 and can just punch the
calculation into his/her calculator. Better yet, challenge them to do the math in
their heads.
I would reduce to 1 x 108/250 x 10-9 then change the numerator to 1000 x 105
then divide and get 4 and combine the exponents according to the rules of
division you subtract exponents. The final answer is 4 x 1014 Hz. Now express
this answer in engineering notation and you get 400 x 1012 Hz and in metric
notation, the frequency of red light is 400 THz (400 Terahertz)
If you want to substitute this into the energy equation for a photon of light with
this frequency, then go back to the meaning of the prefix:
E = h E = 6.63 x 10-34 J s x (400 x 1012 s-1 ) = 2652 x 10-22 J
The proper metric notation would be 265.2 x 10-21 J or 265.2 zJ or zepto joules
When converting prefixes from one prefix to another:
Why would you ever do this in the first place?
To compare numbers?
As an exercise to understanding the meaning?
To express a measurement using the proper prefix after doing a calculation.
Suppose you have a measurement of 0.000 000 300 mm
What would be the proper metric notation?
300 x 10-9 mm = 300 x 10-9 x 10-3 m or 300 x 10-12 meters or 300 pm (pico
meters)
Changing of the prefixes
Or maybe you want to convert a prefix from kilo to micro (just as an exercise)
450 km to micrometers
Do it by the multiplicative identity: 450 x 103 x (106 x 10-6) m = 450 x (103 x 106)
x 10-6 meters. Substitute the prefix micro for 10-6 combine the other numbers and
you end up with 450 x 109 m.
-Advice: When writing exercise, use points of references in science for the
quantities. This way, you can teach two things at once; how to use prefixes in
the metric system and the extremes in science. Nothing travels faster than the
speed of light 3 x 108 m/s.
Metric Prefixes
Learning the Metric System for Meaning
1. Normal Notation (standard decimal notation) - when we write a number to
express a quantity, we do so using commas to make the number easier to read.
We should use spaces (instead of commas) when writing quantities that are less
than one.
a. Express 3 x 108 in normal notation: _________________________________
b. Express 750 x 10-9 in normal notation: _______________________________
2. Scientific Notation – a method used to express numbers as a number
between 1 and 10 multiplied by a power of 10. Scientific notation is used to help
express large and small numbers so that they can be used in calculations easily.
a. Express 102,100,00 in scientific notation: ____________________________
b. Express 0.000 000 000 032 in scientific notation: _______________________
3. Engineering Notation – is like scientific notation except the power of 10 must
be a multiple of 3. This is used so that an appropriate prefix used in the metric
system can be conveniently substituted in for it so that you can express the
quantity in proper metric notation.
a. Express 3 x 108 in engineering notation: _____________________________
b. Express 3.2 x 10-11 in engineering notation: ___________________________
4. Metric Notation – This is when the appropriate prefix is substituted in for the
power of 10.
a. Now express the speed of light in proper metric notation: 300 x 106 m/s
b. Now express the diameter of the helium atom in proper metric notation:
32 x 10-12 m ____________________________________________