Lesson Video: Modeling Hundredths Mathematics • 4th Grade

Video Transcript

Modeling Hundredths

In this video, we’re going to learn how to represent hundredths with a model, a fraction, a decimal, and words.

Let’s look more closely at this model. Here we have one large square. We can call this square the whole amount. And the square has been divided into 100 equal parts or 100 smaller squares. How could we write the shaded amount as a fraction? Well, we know the denominator because our whole amount or large square has been divided into 100 smaller squares or 100 equal parts. So we know the bottom number of our fraction is 100. Each square represents one hundredth. How many squares have been shaded? Each of these columns represents 10 squares. And we know that three 10s are worth 30, and three more squares gives us a total of 33 shaded squares. 33 out of 100 squares are shaded orange, so we would call this fraction thirty-three hundredths.

How could we write thirty-three hundredths as a decimal? Well, we could use our place value table to help us think about the value of each digit. We know this amount is a fraction, and it’s worth less than one, so we can complete the ones column because there are no ones. This part of the number is the whole part of the number. After this number, we have to write a decimal point to separate the whole part of the number from the fraction. We call the part after the decimal the fractional part of the number. So we use the decimal point to separate the whole part and the fractional part.

And to write thirty-three hundredths, we write a three in the tenths column and a three in the hundredths column. Thirty-three hundredths written as a decimal is zero, a decimal point, three, and another three. We would read this as 0.33. We’ve shown thirty-three hundredths using a model. We’ve written it as a fraction and a decimal. To write this amount in words, we would write thirty-three hundredths.

This model shows a mixed number. It has a whole part and a fractional part. In the whole part of our number, we can see that two whole squares have been shaded. And the fractional part of the number shows only part of the whole square has been shaded. We know the whole square has been divided into 100 equal parts or 100 squares, so each column contains 10 squares. So if seven columns are shaded, that represents 70 squares. We know that seven 10s are 70. And there are another five squares shaded, so 75 out of 100 squares are shaded. We call this fraction seventy-five hundredths. So the numbers shown is two and seventy-five hundredths.

How would we write two and seventy-five hundredths as a decimal? We already know that the whole part of the number is worth two, so we can write two in the ones column because we have two whole squares. Next, we need to write the decimal point to separate the whole part of the number from the fractional part. And we know we have seventy-five hundredths. So we would write the seven in the tenths column and the five in the hundredths column. 2.75 is two and seventy-five hundredths.

We made a mixed number using our model. We’ve written it as a mixed number, as a decimal, but how would we write it in words? Well, we know the whole part of the number is worth two and the fractional part of the number is worth seventy-five hundredths. We’ve represented our number using a model, as a mixed number, as a decimal, and in words. Let’s try practicing what we’ve learned now by answering some questions.

The large square represents one whole. Write the fraction that represents the shaded area.

In this question, we’re shown a model of a large square, and we’re told this square represents one whole. We have to write the fraction represented by the shaded part. In other words, what fraction of the square is shaded? Let’s start by thinking about the denominator. The large square has been divided into lots of smaller squares. This is a 100 square. It measures 10 squares by 10 squares. And we know that 10 times 10 is 100. So this is a 100 square. If our whole amount or our large square has been divided into 100 equal parts, then each part is worth a hundredth.

We’re just writing the shaded part. So how many squares out of 100 have been shaded orange? Here’s 10, 20, 30, and seven more. If 37 out of 100 squares have been shaded orange, then the shaded area is thirty-seven hundredths. If the large square represents one whole, the fraction of the square which has been shaded is thirty-seven hundredths.

The large square represents one whole. Write a decimal that represents the shaded area.

In this question, we’re given a large square. This large square measures 10 squares by 10 squares, which means it’s been divided into 100 smaller squares or 100 equal parts. So we know each of the smaller squares represents one hundredth. So to help us find the decimal that represents the shaded area, we need to know how many of these smaller squares have been shaded. We need to know how many hundredths are shaded. There are 10 squares in each column, so let’s count in tens. 10, 20, 30, 40, 50. And one more shaded square makes 51. 51 out of 100 squares are shaded.

We’ve written the shaded area as a fraction. How would we write it as a decimal? We know the large square represents one whole, and fifty-one hundredths have been shaded, so we know our number is less than one. In other words, it has zero ones. And we know the fractional part of our number is fifty-one hundredths, so we can write our five digit and our one digit to represent fifty-one hundredths. The decimal which represents the shaded area is fifty-one hundredths, which we write as 0.51.

Each big square is one whole. Daniel has colored two wholes and seventeen hundredths orange. Write this as a mixed number. Write this as a decimal. Tip: Use a place value table to help you.

We know that Daniel has colored two wholes and seventeen hundredths orange. We have to write this amount as a mixed number and as a decimal, and we’re told to use the place value table to help. How would we write two wholes and seventeen hundredths as a mixed number. We know that each big square is one whole, and we also know that Daniel has colored two whole squares or two big squares orange, so the whole part of his mixed number is two. We also know that the fractional part of his number is seventeen hundredths. The large square has been divided into 100 smaller squares or 100 equal parts, and each part is a hundredth. And we know that Daniel has colored seventeen hundredths, so two wholes and seventeen hundredths written as a mixed number is two and seventeen hundredths.

Now we need to write this as a decimal. We know that Daniel has colored two whole squares, which represent two ones. And the fractional part of the number is seventeen hundredths. So two wholes and seventeen hundredths as a decimal is 2.17, which we would say as two and seventeen hundredths. Daniel colored two wholes and seventeen hundredths orange. We would write this as a mixed number as two and seventeen hundredths. And to write this as a decimal, we would write 2.17, which is two and seventeen hundredths.

What have we learned in this video? We have learned how to represent hundredths with a model, a fraction, a decimal, and in words.