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

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

13:52

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.

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