We're determining the length of each bar.
First thing we should notice is that the units
are centimeters, and whenever expressing a length
it is important to include the units.
Next, notice how each centimeter is partitioned
or cut into smaller equal pieces.
Notice there are 10 tick marks between each centimeter
and therefore each tick mark represents
1/10 of a centimeter.
And we'll express our lengths both in decimal notation
as well as using fractions just to make a connection.
It is normally common to express a length
in centimeters using decimal notation.
So starting here we can count the number
of whole centimeters here, one, two,
three, four, five,
six, seven, eight,
nine, 10.
You'll notice how the length is longer
than 10 centimeters.
So from here we can count the number of tick marks,
which again, each tick mark represents
1/10 of a centimeter.
So we have one, two, three, four, 5/10 of a centimeter
longer than 10 centimeters, so the total length
would be 10 5/10 of a centimeter, which we can write
as 10.5 centimeters
using decimal notation,
or in fraction notation we could say 10 5/10 centimeters.
We normally don't express a mixed number in this form
because this fraction can be simplified,
meaning we can use larger partitions than 10ths
to express this length as a mixed number.
So going back to the ruler, we know from 10 centimeters
to 11 centimeters is one centimeter.
So if we partition this length into smaller lengths,
let's say half centimeters here, we can see this length
is exactly 10 1/2 centimeters.
So instead of 10 5/10 it would be better to express this
as 10 1/2 centimeters.
And again, normally when expressing length in centimeters
we do only express it using decimal notation
or this notation here.
Let's take a look at our second example.
Starting here, again we'll count the number
of complete centimeters.
So one, two,
three,
four,
five,
six,
seven,
eight,
nine,
10,
11,
12,
13, 14, and again, then length is longer
than 14 centimeters.
So let's count the number of tick marks.
It might be hard to see on the screen,
but we have 1/10, 2/10, 3/10, 4/10
of a centimeter longer than 14 centimeters.
So we have 14 4/10 centimeters,
which we can write using decimal notation
as 14.4 centimeters,
or using mixed numbers we could say 14 4/10.
And again, we can simplify 4/10 or express this
using larger partitions.
If you look at the centimeter from 14 centimeters
to 15 centimeters you know it's already divided
into 10 equal pieces.
So if we partition this one centimeter
into five equal partitions, each partition consisting
of 2/10 of a centimeter, we'd have a partition here,
here,
here, and here.
It's probably hard to see.
That would be 2/5 of a centimeter,
so it's better to express 4/10 as 2/5.
Another way to do this would be to start with 4/10
and divide out the common factor of two.
Four divided by two is two, 10 divided by two is five.
So 4/10 is equivalent to 2/5,
but 2/5 is a simplified fraction
and therefore the best way to write this as a mixed number.
But once again when expressing a length using centimeters,
we're mainly only concerned about the decimal notation.
I hope you found this explanation helpful.