### Video Transcript

Decimals on Number Lines:
Tenths

In this video, we’re going to learn
how to locate tenths on a number line and record them with fractions and
decimals. This strip of paper represents one
whole. If we divide this strip into 10
equal parts, we call this one-tenth. We know how to write one-tenth as a
fraction. But do you know how to write it as
a decimal?

To write the shaded part as a
fraction, we would write one over 10 or one-tenth. When we write this as a decimal, we
would write a zero followed by a decimal point and a one digit. And we would read this as one-tenth
or 0.1. As well as a part–whole model or
fraction strip, we can represent fractions on a number line. You can see a number line starts at
zero and ends at one. And each interval along the number
line represents one-tenth. So we would mark one-tenth on the
number line here.

This fraction strip shows
six-tenths. How would we write that as a
decimal? Zero, because it’s less than one
whole, a decimal point, and a six. We’ve written six-tenths as a
fraction and a decimal. But where would we mark it on our
number line? We’ve marked one-tenth. So we can count forward in tenths:
one-tenth, two-tenths, three-tenths, four-tenths, five-tenths, six-tenths. And we can mark six-tenths here on
the number line.

How would we write this amount as a
decimal and a fraction? This represents one whole, and this
is a fraction of a whole. So we know our number is greater
than one or worth more than one. We’ve got one whole and
three-tenths. So we would write this as a mixed
number, the whole amount and the fraction of a whole amount. How would we write this as a
decimal?

Well, we write the whole amount or
one before the decimal point and we write the tenths or the fraction of a whole
amount after the decimal point. One, a decimal point, and the
number three is how we write one and three-tenths as a decimal. Where would we write one and
three-tenths on our number line? This time, instead of starting at
zero, we’re starting at one. One and three-tenths would be
between one and two on our number line. And we know that each division is
worth one-tenth. So we need to count forward
three-tenths along the number line: one, two, three. This is where we would write one
and three-tenths. We can mark it on the number line
as a decimal and as a fraction.

Now that we’ve learned how to write
tenths as fractions or decimals and how to locate decimals on a number line, let’s
try answering some questions.

Look at the number represented by
the number line. Write this number as a mixed
number. Write this number as a decimal.

In this question, we have to write
the number represented on the number line as a mixed number and as a decimal. This number line starts at two and
zero-tenths and ends at three and zero-tenths, which means that each division on the
number line represents one-tenth. So we know that our number is
between the two whole numbers two and three. We can see that it’s more than two,
but not quite three. So we know the first part of our
mixed number is two, but two and how many tenths? One, two, three, four, five, six,
seven, eight. So the number represented by the
number line written as a mixed number is two and eight-tenths.

How would we write this number as a
decimal? The number which comes before the
decimal point is the whole number. And we already know that this is a
two. What would we write after the
decimal point to represent our eight-tenths? We would write an eight digit. This is worth eight-tenths. We wrote 2.8 to represent two and
eight-tenths. First, we identified the number
represented on the number line. We wrote it as a mixed number and
as a decimal.

Which point on the number line
represents two and three-tenths?

In this question, we’re given a
number line and we have three points marked, point 𝐴, 𝐵, and 𝐶. We have to identify which point
represents two and three-tenths or 2.3. Each of the three points is between
two and zero-tenths and three and zero-tenths. So we know that each of our points
is worth two and an amount of tenths.

We’re looking for the point which
represents two and three-tenths. Each division on this number line
represents one-tenth. So this division represents two and
one-tenth. So the next division would be two
and two-tenths. So we know that point 𝐴 isn’t the
correct answer. Point 𝐵 represents two and
three-tenths. Let’s keep counting to see what
point 𝐶 represents: 2.4 or two and four-tenths, two and five-tenths, two and
six-tenths. The point on the number line which
represents two and three-tenths is point 𝐵.

Which decimals are marked on the
number line?

In this question, we’ve been given
a number line and we have to identify these four decimals, which have been marked on
the number line. The first two decimals are marked
between the numbers 18 and 19 on the number line. So we know the whole number which
comes before the decimal point in both of the missing decimals is 18.

Before we can write the decimal
amount, we need to work out what each division on the number line is worth. There are 10 divisions between the
numbers 18 and 19, which means that each division is worth one-tenth: 18 and
one-tenth, 18 and two-tenths. So our first decimal is 18 and
three-tenths.

Let’s keep counting until we reach
our next decimal: 18 and four-tenths, 18 and five-tenths, 18 and six-tenths, 18 and
seven-tenths. We wrote the whole number before
the decimal point and the tenths after the decimal point. So we found our first two
decimals.

Our next two decimals are between
the whole numbers 19 and 20. The first orange point shows us
where 19 is or 19 and no tenths. So the next division is 19 and
one-tenth. Let’s keep counting forward in
tenths: 19 and two-tenths, 19 and three-tenths, 19 and four-tenths, 19 and
five-tenths. The decimals marked on the number
line are 18 and three-tenths, 18 and seven-tenths, 19 and one-tenth, and 19 and
five-tenths. We counted along the number line in
tenths to help us find the missing decimals.

What have we learned in this
video? We have learned how to write an
amount of tenths as a fraction and as a decimal. We have also learned how to locate
tenths on a number line.