Comparing Decimals: Tenths and Hundredths
Basics on the topic Comparing Decimals: Tenths and Hundredths
Comparing Decimals – Tenth and Hundredth
When comparing decimals tenths and hundredths, use the greater than, less than, or equal to symbols.
In this text on comparing decimals, we practice comparing decimals with models in addition to looking at place value, because base ten blocks help us visualize numbers. Let’s take a look at a comparing decimals example.
Revision – Tenths and Hundredths
Remember, when we talk about decimals, we talk about numbers smaller than 1 (0.86, 0.65, …). The tenth place in a decimal number is the first number after the decimal point. The hundredth place in a decimal number is the second number after the decimal point. Let’s look at an example – 0.57 – in a place value chart.
| Ones | Decimal point | Tenths | Hundredths |
|---|---|---|---|
| 0 | . | 5 | 7 |
Comparing Decimals – Example
The first labels they have to compare are twenty-five hundredths and eight tenths. Below, we have twenty-five out of one hundred squares shaded in, and eight out of ten strips shaded in.
When comparing decimals you need to start with the greatest place value, the ones place. Since the zeros are equal, we move to the next place value, the tenths place. Twenty-five hundredths has a two in the tenths place, and eight tenths has an eight in the tenths place.
Since we found a digit greater or less than, we can stop comparing! Twenty-five hundredths is less than eight tenths.
Comparing Decimals – Summary
Remember, when comparing decimals keep these steps in mind:
| Step # | What to do |
|---|---|
| 1 | Start with the greatest place value, and compare. |
| 2 | If the digits are equal, move on to the next place value. |
| 3 | Repeat the process until you find a digit that is greater than or less than and compare using the greater than or the less than symbol. |
| 4 | If the digits are the same and the value shaded in is equal, that means the decimal numbers are equal. |
| 5 | Compare using the equal to symbol. |
- Start with the greatest place value, and compare
- If the digits are equal, move on to the next place value
- Repeat the process until you find a digit that is greater than or less than and compare using the greater than or less than symbol
- Or, if the digits are the same and the value shaded in is equal, that means the decimal numbers are equal
- Don't forget to compare using the equal to symbol.
Have you practiced yet? On this website you can find more interactive exercises, worksheets and more activities on comparing decimals to the tenths and hundredths.
Transcript Comparing Decimals: Tenths and Hundredths
"Whew! Our first day on the job is going swimmingly!" "Turtally! Except (...) our day just got started." "Erm, right. Look! We have to compare the numbers on the labels to sort the packages into bins." "The equal packages go in this bin... the smaller value packages go in THIS bin... and the larger value packages go in THIS bin!" Let's help Axel and Tank by... Comparing Decimals: Tenths and Hundredths A decimal number represents an equal part of a whole, just like a fraction. To compare decimals, use the greater than (...) less than (...) or equal to symbols. The first labels they have to compare are twenty-five hundredths and eight tenths. Base ten blocks help us visualize numbers, so let's use them to compare the decimals. HERE, we have twenty-five out of one hundred squares shaded in... and HERE, we have eight out of ten strips shaded in. Now, compare starting with the GREATEST place value, the ONES place. Since the zeros are EQUAL, we move to the next place value, the TENTHS place. Twenty-five hundredths has a two in the tenths place... and eight tenths has an eight in the tenths place. Since we found a digit greater or less than, we can stop comparing! Twenty-five hundredths is LESS THAN eight tenths. Next, Axel and Tank need to compare six tenths and sixty hundredths. Let's represent them using base ten blocks. HERE, we have six out of ten STRIPS shaded in... and HERE, we have sixty out of one hundred SQUARES shaded in. Now, start by comparing the GREATEST place value, the ONES place. Since the zeros are EQUAL, move to the next place value, the TENTHS place. Both numbers are equal, so we move to the HUNDREDTHS place. Six tenths doesn't have a number in the hundredths place, so write a zero as a placeholder. What do you notice about the HUNDREDTHS place? (...) There are two zeros, making these decimals EQUAL (...) because ALL the place value digits are the SAME. How is that possible? (...) Even though the wholes are broken into different parts, both values are equal! Last, Axel and Tank need to compare one and twenty-nine hundredths and one and two tenths. Let's represent them using base ten blocks. HERE, we have one whole and twenty-nine out of one hundred squares shaded in... and HERE, we have one whole and two out of ten strips shaded in. What is the first step? (...) Start by comparing the GREATEST place value, the ONES place. Since the ones are EQUAL, we move to the TENTHS place. What do you notice about the TENTHS place? (...) Both numbers are equal, so we move to the HUNDREDTHS place. One and two tenths doesn't have a number in the hundredths place, so write a zero as a placeholder. What do you notice about the HUNDREDTHS place? (...) One and twenty nine hundredths has an nine in the hundredths place... and one and twenty hundredths has a zero in the hundredths place... so one and twenty nine hundredths is GREATER THAN one and twenty hundredths. It looks like one more package came down the belt, and it has Axel and Tank's names on it! Before we see what's inside let's summarize. Remember, (...) when comparing decimals... start with the GREATEST place value, and compare. If the digits are equal, move on to the next place value. Repeat the process until you find a digit that is greater than or less than... and compare using the greater than or less than symbol. Or, if the digits are the same and the value shaded in is equal, (...) that means the decimal numbers are EQUAL. Don't forget to compare using the equal to symbol. "I can't believe we got these groooovy costumes!" "Yeah! Let's go explore beneath the waves!"
Comparing Decimals: Tenths and Hundredths exercise
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Where do we start comparing?
HintsThink about place value. Can you identify the largest place?
When looking at a number, you read it left to right
Remember, decimals are equal parts of a whole.
Base ten blocks help us visualize decimals. Grab a piece of paper and draw the models.
SolutionThe correct answer is greatest place because you want to start comparing the digits left to right. This means starting with the greatest place. When comparing the decimals 0.25 and 0.8 as shown in the model, we start in the ones place because that is the greatest place. Since both decimals have a 0 in the ones place, we would then move on to the next place, the tenths place to compare.
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Match the base ten model to the decimal it represents.
HintsRemember a tenth means a full row will be shaded in on the base ten model.
Use this model as a guide. The decimal 0.76 has a 7 in the tenths place, so 7 full rows are shaded in. The 6 is in the hundredths place, so 6 individual squares are shaded in.
A model that is entirely shaded in represents one whole.
Remember a decimal is part of a whole.
Solution0.27 is represented by a model cut into 100 squares. Since the 2 is in the tenths place, 2 full rows need to be shaded in. Since the 7 is in the hundredths place, 7 individual squares need to be shaded in.
0.8 is represented by a model cut into 10 rows. Since there is an 8 in the tenths place, 8 rows need to be shaded in.
1.15 is represented by two models cut into 100 pieces. Since the 1 is in the ones place, one whole model needs to be shaded in. .15 is represented by shading in one full row or one tenth and 5 individual squares for the 5 in the hundredths place.
0.12 is represented by a model cut into 100 pieces. One full row is shaded in to represent 1 tenth. Two individual squares are shaded in to show the 2 in the hundredths place.
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Which decimals are greater than 0.74?
HintsGreater than means bigger or larger.
Start to compare with the greatest place. In this picture you can see that both decimals have a 0 in the ones place. That is not enough to compare, so move to the right and compare the digits in the tenths place.
You are comparing a 2 and 8. 2 is less than 8, so 0.25 is less than 0.8
If the decimals don't go to the same place, add a 0 as a place holder.
0.60 goes to the hundredths place and 0.6 goes to the tenths place. We can add a 0 in the hundredths place to make the decimal 0.60. You then see that these are equal.
Grab paper and pencil and draw base ten models of each decimal and compare it to the model for 0.74.
SolutionIn the image above, we can see that 0.8 is greater than 0.74. This is because when you compare the tenths place, 8 is larger than 7. In the model you see 8 rows fully shaded compared to 7 rows fully shaded.
The remaining solutions are:
- 0.77 > 0.74; when you compare the hundredths place, you will find that 7 is greater than 4 which shows that 0.77 is greater than 0.74.
- 1.74 > 0.74; when you compare the ones place, you will find that 1 is greater than 0. One whole shaded in compared to no wholes shaded in makes 1.74 larger.
- 0.97 > 0.74; when you compare the tenths place, you will find that 9 is greater than 4; which shows that 0.97 is greater than 0.74.
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Compare the decimals using >, <, =
HintsStart comparing by looking at the digit in the greatest place.
Remember all decimals must go to the same place. Use zero as a place holder if they do not go to the same place.
The model below shows that 1.54 < 1.65. When looking at the model, you compare the tenths place which are full rows shaded in. The model on the left has five full rows shaded in and the model on the right has six full rows shaded in. Five is less than six.
SolutionThe correct answers are:
- 0.63 > 0.51 because 6 tenths is more than 5 tenths
- 1.4 = 1.40 if you add a zero to the hundredths place in 1.4, you see that the decimals are the same
- 1.07 < 1.70 because 0 tenths is less than than 7 tenths
- 0.80 > 0.08 because 8 tenths is more than 0 tenths
- 0.76 < 0.9 because 7 tenths is less than 9 tenths
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Compare the decimals using models.
HintsStart with the greatest place value and compare. If the digits are the same, keep moving to the next place value until the digits are different.
Remember when decimals don't go to the same place, add a 0 as a place holder and then compare.
In the example, we start by comparing the ones place. They have the same digit, so we move to the tenths place which also have the same digit. So, we move to the hundredths place. 1.2 doesn't have a digit in the hundredths place, so we add a 0 as a place holder and then compare. 9 hundredths is greater than 0 hundredths, so 1.29 > 1.2
SolutionDecimal models help us visualize decimals and compare them. Based on the models given the correct pairs are:
- 0.8 > 0.6; 8 tenths is greater than 6 tenths
- 0.6 = 0.60; these decimals are equal because when you add a zero to 0.6 it becomes 0.60. Therefore 0.6 and 0.60 are the same.
- 0.1 < 0.4; 1 tenth is less than 4 tenths
- 0.68 > 0.32; 68 hundredths are greater than 32 hundredths
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Greater than, less than, or equal to?
HintsStart with the greatest place when comparing.
Make sure the decimals go to the same place.
If the digits are the same, move on to the next digit to compare.
Solution- 1.24 and 1.4 are greater than 1.2 so you assign them to the > symbol.
- 1.02 and 0.24 are less than 1.2 so you assign them to the < symbol
- 1.2 and 1.20 are equal to 1.2 so you assign them to the = symbol
I like decimals