As I said we’re gonna start with some tools
and skills for quantitative thinking because
this will be very useful for you as we move ahead
just to have a sort of a quantitative toolbox
for you as we go. This will help you to solve
problems. It will be very key skill to have,
especially in exam setting, in which it will help
you to move much more quickly through the material.
The three things that I would like to make sure
to cover are, first, scientific notation and
how we write numbers and can use it in problems.
Second, unit analysis, how we can just look at
the units of key variables we’ll introduce,
an example of which is here which you do not
need to memorize yet. And how we’ll be able to
use unit analysis in problems and sometimes
be able to solve entire difficult looking problems
just by analyzing the units in front of us.
And then finally, I would like to introduce and
help practice a key mindset, which is the mindset
of proportionalities, understanding how one quantity
can depend on another in a particular way
can help you to solve seemingly difficult problems
very very efficiently and quickly.
So let’s see what these three skills are.
First in sciences and certainly in physics, and also
will be the case in medicine, we deal with very
very big numbers. Sometimes these numbers have
many digits as this number right here does
before the decimal point and sometimes they’ll
even be very very small numbers. Because we don't
want to write huge numbers all the time
over and over again, we introduce a notation,
a particular way of writing numbers.
This way of writing numbers that we’re gonna use
is called scientific notation, it comes form the
basic fact that in our system which it’s a based
ten system. When you multiply a number by ten,
it just gets a zero added to it. We can use
this fact to rewrite a number as big as this one
just by moving the decimal point from one end
all the way back so instead of writing two, three,
four and then a lot of zeros, we can just write
2.340 and tell you how many tens you need to
multiply by to get back to the original big number.
Practically, in order to do this, you just take
your decimal point, move it over as many places
as you need to, counting as you go and however
many places you need to move that decimal point,
that’s how many power of ten you’re gonna need.
In this case we have to move the decimal point
12 places over and so the actual number written
in scientific notation is 2.340 times 10 to the
power of 12. In scientific notation we have a
convention which is that you always put the
decimal point right after the first non zero digit.
And in this number, the first digit that is not zero
is a 2, and so we’ll move the decimal point over
until we reach the 2, then we stop the decimal place
after the 2. Once we’ve done that, we can write
many many big numbers in scientific notation.
This will be very useful as we go forward.
We get to see the usefulness of scientific notation
immediately right now because we’re dealing with
so many big numbers and so many small numbers
that we introduce some notation and some names
for powers of 10 that we see very often.
An example you might be familiar with is kilo,
this 10 to the third on the first column you see
on your left. This kilo is something you might
have heard of with kilograms. We don’t like
measuring masses that, that small as grams or maybe
kilometers here, or maybe a meter is too small when
you’re talking about something like driving long distances
and so we introduce a prefix, kilo, which tells us
that we’re talking about, not meters but thousands
of meters or kilometers. As we go forward, in fact,
the right column here, the one with the lower case
prefixes like deci, and centi, and milli, et cetera.
are actually gonna be more useful as we go forward
in terms of how commonly they come up.
I’d like to draw your attention to
milli, micro and nano. These are ones that are
probably the least familiar initially for people
but also come up the most often. And so you
wanna really practice using those. In terms of
writing numbers using this notation, what you
wanna do is take your numbers, say it a very
small number of seconds, like a millisecond and
instead of writing 0.001 seconds, you can say that
it’s one millisecond. And the way you write that
unit you can see, in the far right column, with m.
The letter m you just put it in front of the letter
s and that will tell people that it’s milliseconds.
And you’ll be able to see and use
all these notations as we go forward.