Lesson Video: Decimals on Number Lines: Tenths | Nagwa Lesson Video: Decimals on Number Lines: Tenths | Nagwa

# Lesson Video: Decimals on Number Lines: Tenths Mathematics • 4th Grade

In this video, we will learn how to locate tenths on a number line and record them with fractions and decimals.

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### 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.