Video Transcript
Decimals on Number Lines:
Hundredths
In this video, we will learn how to
locate hundredths on a number line and record them with fractions and decimals. Both of these number lines show the
number 3.75. If we were to write 3.75 as a mixed
number, the whole part of the number is the digit three and the fractional part of
the number is seventy-five hundredths. Our first number line starts at 3.0
or three and ends at four or 4.0. And we know that our number is
worth more than three but less than four. Each division on the number line
represents one-tenth: 3.1 or three and one-tenth, 3.2, 3.3, and so on.
So far, we’ve reached 3.7, which is
the same as three and seventy hundredths. So 3.75 comes halfway between 3.7
and 3.8. 3.75 is halfway between 3.70 and
3.80. Our first number line has been
marked in tenths. And this is how we would show 3.75
on this number line. Our second number line has been
divided into hundredths. We know that 3.75 is halfway
between 3.70 and 3.80.
So to divide our number line into
hundredths, we started at 3.70, and the last number on our number line is 3.80. This number line goes up by one
hundredth each time: 3.70, 3.71, 3.72, 3.73, 3.74, and we’ve reached 3.75. Both of our number lines show 3.75,
but the divisions on the number line have been marked differently. The first is in tenths. The second is in hundredths.
How could we show 0.67 on this
number line?
We can see from our place value
table that 0.67 has no ones, so we know it’s worth less than one. So we could mark the number zero
and one on our number line. Halfway between these two numbers
would be 0.5, which is the same as a half, or fifty hundredths. Each division on the number line is
worth a tenth. We start counting at zero. The next number on the number line
is 0.1, 0.2, 0.3, and so on until we reach number one.
We know that 0.67 has a six in the
tenths place, so 0.67 will come somewhere between 0.6 and 0.7 or 0.60 and 0.70. Each of the smaller divisions we’ve
marked is worth one hundredth. So 0.67 would go here on our number
line. This number line has been divided
into hundredths, starting at 0.60 and ending at 0.70. Each division is worth a hundredth,
so we would mark 0.67 here. So far, we’ve learned that to mark
decimal numbers onto our number line, we can either count in tenths or in
hundredths. Let’s try answering some questions
now to put into practice what we’ve learned so far.
Look at the highlighted number on
the number line. Write this number as a mixed
number. Write this number as a decimal. Tip: Use a place value table to
help you.
In this question, we’re given a
number line and the pink arrow shows the highlighted number. We can see where this number has
been marked on the number line, but we don’t yet know what this number is. So first, we have to work out which
number is shown on the number line. Then we have to write it as a mixed
number and then as a decimal. The numbers written on the top of
the number line are mixed numbers. The numbers on the bottom of the
number line are decimals, so our number comes between the whole numbers three and
four.
Let’s stop and look more closely at
the mixed numbers at the top of our number line. We start with three and no
hundredths. Then we have three and twenty
hundredths, three and forty hundredths, three and sixty hundredths, three and eighty
hundredths, and four and no hundredths. So we’re adding twenty hundredths
each time. And the decimals at the bottom also
go up in twenty hundredths or two-tenths each time: three, 3.2, 3.4, 3.6, 3.8. So each of these marked intervals
is worth 0.20 or twenty hundredths. The highlighted number comes
between 3.6 and 3.8 or three and sixty hundredths and three and eighty
hundredths. And the number which comes halfway
between these two numbers is 3.7 or three and seventy hundredths.
So let’s keep counting from three
and seventy hundredths till we reach the highlighted number. We’re going to count on in
hundredths. So we’re starting at three and
seventy hundredths, seventy-one hundredths, seventy-two, seventy-three,
seventy-four, seventy-five, seventy-six, seventy-seven, seventy-eight. So the highlighted number is three
and seventy-eight hundredths, which we’ve written as a mixed number.
How would we write this as a
decimal? Let’s follow the tip and use the
place value table to help us. We know the whole part of our mixed
number is worth three ones, and we would write our seventy-eight hundredths after
the decimal point. We identified the highlighted
number on the number line. We wrote it as a mixed number and
as a decimal. The highlighted number is 3.78.
What decimals are marked on the
number line?
In this question, we’ve been given
a number line. We have to find the decimals which
have been marked. So we have to find the four missing
decimals. The number line begins with 21.67,
and the last number is 21.87. And the number which is halfway in
between these two numbers is 21.77. We can see that the hundredths are
increasing. We know the difference between
sixty-seven hundredths and seventy-seven hundredths is ten hundredths. And as there are 10 divisions, we
can count in hundredths. So if we start at 21.67, the next
number on the number line will be 21.68, 21.69, 21.70, 21.71, 21.72. So our first missing decimal is
21.73.
Let’s keep counting, 21.74, 21.75,
21.76. Let’s keep counting forward to find
the next missing number. We can start at 21.77,
seventy-eight hundredths, seventy-nine, eighty, eighty-one, eighty-two. This missing decimal is 21.82,
eighty-three, eighty-four, eighty-five hundredths. The final missing decimal is
21.85. We worked out what each of the
divisions on the number line was worth and counted forward in hundredths to find the
missing decimals, which are 21.73, 21.76, 21.82, and 21.85.
Which point marked on the following
number line represents 0.35?
In this question, we’re given a
number line which has three points 𝐴, 𝐵, and 𝐶 already marked. We have to select the point which
represents 0.35. Is it point 𝐴, 𝐵, or 𝐶? Let’s try and work out what each
interval on the number line is worth. So we start at zero and go up to
0.25, 0.50, 0.75, and another twenty-five hundredths takes us to one whole or a
hundred hundredths.
So if the difference between each
of our numbers is twenty-five hundredths, what is each division worth? It must be five hundredths: zero,
0.5, 0.10, 0.15, 0.20, 0.25. So we know that point 𝐴 represents
0.15. We’re looking for the point which
shows 0.35. Now that we’ve eliminated point 𝐴,
we know it’s got to be 𝐵 or 𝐶. Let’s carry on counting from 0.25:
0.30, 0.35. Point 𝐵 represents 0.35 and point
𝐶 represents 0.40. Out of our three points marked on
the number line, the one which represents 0.35 is point 𝐵. We worked out what each division on
the number line was worth. And we counted forward in five
hundredths each time until we found the point which represented 0.35. Point 𝐵 shows 0.35.
What have we learned in this
video? We’ve learned how to locate
hundredths on a number line and record them with fractions and decimals.
