hi I'm Rob welcome to math antics in a
previous video we learned about the most
common units for measuring distances in
this video we're going to talk about how
you actually use some of those units
when making a measurement in real life
making measurements is something you
would typically learn how to do in
science class but since measurement uses
math to get the job done it's often
taught in math class too so here we go
suppose were given an object like this
pencil and we're asked to measure its
length in centimeters to do that we need
some method or device that will tell us
how many centimeters long the pencil is
remembering that a centimeter is roughly
the width of a pinky finger I could just
use my finger as that device and see how
many finger widths it takes to get from
one end of the pencil to the other but
something a little more accurate would
be nice and that's where a ruler comes
in handy I the Great King Robb ruler of
all the land declare that the span of my
royal hand shall henceforth be the
measure of all things in my kingdom
great or small ah not that kind of a
ruler in math and science a ruler is a
flat piece of material that has markings
on it that correspond to standard units
of distance for example this ruler has a
series of markings that correspond to
inches on one side and centimeters on
the other that's cool we'll just ignore
the inches side and use a centimeter
sight for this measurement we start by
moving the ruler so that the zero
centimeter mark is aligned as closely as
we can with one end of our pencil then
we'll see where the other end of the
pencil lies on the scale of centimeters
looking at the numbers you can see that
the other end lines up nicely with the
19 centimeter mark so this pencil is 19
centimeters long but what if the pencil
gets sharpened and then used and
sharpened and used again so that it gets
shorter
now if weari measure it with our ruler
you'll see that we have a small problem
the tip of the pencil doesn't line up
with any of the centimeter marks anymore
they lie somewhere between the 17 and 18
centimeter marks we could just say that
it's between 17 and 18
centimetres long but it would be nice if
we could be a little more accurate than
that being more accurate means making a
measurement that is closer to the true
value fortunately most rulers divide the
space between each centimeter mark into
ten equal parts that represent
millimeters which are exactly one tenth
of a centimeter because the millimeter
marks are so much smaller
they don't have numbers on them but if
you look closely it will be able to
count that there are nine smaller lines
that divide the centimeter into ten
equal parts the middle of these nine
lines is usually a little longer than
the rest so that it's easier to tell
where the halfway point is using these
subdivision marks we can get a more
accurate measurement of the length of
our sharpened pencil do you see how the
pencils tip almost lines up with the
third subdivision line that comes right
after the 17 centimeter mark that means
that the length of the pencil is 17
centimeters plus 3 millimeters or 17.3
centimeters well that's a pretty close
measurement but remember the tip of the
pencil didn't line up exactly with the
third subdivision line it went just a
little bit past it our ruler doesn't
have markings smaller than a millimeter
so it will be hard for us to make a
measurement more accurate than that but
we could make an estimate for example it
looks like the pencil tip goes past the
three millimeter mark by a very small
amount maybe just a tenth of a
millimeter so we could estimate that
it's length is closer to 17.31
centimeters if you really did need a
more accurate measurement you need to
use a better measurement device that can
provide that level of accuracy for
example calipers and micrometer x' are
devices that can measure distances as
accurate as a tenth or even a hundredth
of a millimeter and certain measurement
techniques using lasers can achieve even
higher accuracy x' down to extremely
small units like nanometers those more
advanced types of measurements are
beyond the scope of this video but
hopefully they'll help you realize
something fundamental about the nature
of measurement you can't measure the
exact value of something there's always
a limit to the accuracy you can achieve
based on your measurement device
accuracy is basically how close a
measured value is to the true value and
a measurement the idea is to get as
close as possible or at least as close
as you need for your
purposes luckily I didn't really need to
know the length of this pencil down to
the nearest tenth of a millimeter in
fact I didn't really need to know its
length at all since I'm just gonna write
with it okay now that you understand
what accuracy is and we've made a
measurement that was accurate to the
nearest centimeter as well as one that
was accurate to the nearest millimeter
let's try making a measurement with the
non metric side of our ruler which
measures inches suppose we want to know
the length of this toothbrush in inches
to measure that we first line up one end
of the toothbrush with the start of the
inches scale on the ruler which
represents zero inches then we see where
the other end of the toothbrush lies on
that scale notice it's somewhere between
seven and eight inches can we get a more
accurate measurement than that yup
fortunately as was the case with
centimeters on the other side of the
ruler inches are usually subdivided into
fractions of an inch also on this
particular ruler each inch is subdivided
into eight equal parts that means our
toothbrush is not quite as long as seven
and three-eighths of an inch but it's a
little longer than seven and two eighths
of an inch which would be equivalent to
seven and one quarter inches
whoa whoa whoa what are you talking
about with all these fractions I thought
this video was about measurement not
fractions well yes but when things don't
line up exactly with the particular unit
to get more accuracy you need to use
fractions of that unit the metric system
makes that look easy because things are
always divided by ten so the fractions
match up really nicely with our base ten
decimal system but English or American
units have traditionally been divided up
differently so the fractions you use for
them are a little bit trickier so you're
saying this is all America's fault well
American didn't invent the system it's
just a traditional system of units that
goes way back in history to the days of
monarchies so I guess it's probably some
Kings fault how dare you anyway it's
true that the traditional way of
subdividing inches is kind of messy when
compared to the metric system so we'll
help if we take a closer look basically
there's two ways that inches are
commonly subdivided one is base
on dividing by 10 and the other is based
on dividing by 2 we'll start with the
system that's based on dividing by 10
because that sounds a lot like the
metric system doesn't it it turns out
that an inch can be divided up in a
metric like way even though an inch is
not a metric unit here's how that works
you start with an inch and then divide
it into ten equal parts each mark
represents 1/10 of an inch so you can
express the fractional parts easily with
decimal digits just like you do with the
metric system for example if the
measurement came out to be one and two
tenths inches you just say it's one
point two inches or if a measurement
came out to be five and eight tenths
inches you just say it's five point
eight inches you know when you need more
accuracy you can keep subdividing by ten
so that you'd get hundredths of an inch
thousandths of an inch
ten thousandths of an inch and so on
this way of dividing up inches is
commonly used in American engineering
since it has many of the benefits of the
metric system even though it's based on
inches the other way of dividing up
inches which is still commonly used in
American construction is to divide them
up by two here's how that system works
you start with an inch and then divide
it into two equal parts that means you
can now measure to an accuracy of half
an inch then you divide those half
inches by two so you can measure to an
accuracy of a quarter of an inch then
you divide those quarter inches by two
so you can measure to an accuracy of an
eighth of an inch and you keep going
like that dividing by two again let you
measure to an accuracy of 1/16 of an
inch
and dividing by two again let you
measure to an accuracy of 1/32 of an
inch and so on the basis of these
fractional parts of an inch are all
different but they're all powers of two
it's actually a really logical system if
you think about it but it has the
disadvantage that it's harder to convert
to decimal values when you need them
it's also harder to add and subtract
measurements if the fractions don't have
the same base when things are divided by
ten it's easy because we use decimal
number places that are specifically
designed for counting fractions like
tenths hundredths and thousandths but we
don't have number places for halves
quarters and eighths instead it's very
common for people who use a lot of these
traditional fractions of an inch
to just memorize some of the most common
equivalent decimal values and use a
calculator to convert the rest for
example they might memorize things like
1/2 equals 0.5 1/4 equals 0.25 and 1/8
equals 0.125 now that you know the two
main ways of dividing up inches let's go
back to our toothbrush example if we use
a ruler that has divisions of 1/16 of an
inch
you can see that it's length is about 7
and 5/16 of an inch that should be
plenty accurate for brushing my teeth so
now you know the basics of how you use a
ruler to make measurements but you may
need to brush up on your fractions to be
successful in it see what I did there
last of all I want to briefly introduce
you to some low-tech devices that are
commonly used to measure longer
distances for example a tape measure is
sort of a long flexible ruler that can
be wound up on a spool to make it more
compact it's a really handy device and
carpenters use them all the time when
you unwind it you can measure much
longer distances in the same way you
would with a ruler and it's a lot more
convenient than carrying around a 10
meter stick
there's another cool device often called
a measuring wheel that can be used to
measure even longer distances by rolling
a wheel along the ground or any surface
it has a counter on it that tallies up
each foot or meter that you roll it past
so you can measure the total distance
traveled of course there are lots of
high-tech methods for measuring
distances nowadays - and your phone can
probably keep track of how many miles
you've traveled in a day and where you
went and who you talk to and what you
might like and might want to buy and and
who you have a crush on it alright
that's the basics of measuring distance
remember the way to get good at math is
to actually practice it so get on out
there and start measuring stuff as
always thanks for watching math antics
and I'll see you next time you heard the
man practice learn more at math antics
com