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