# Comparing Decimal Tenth and Hundredth

Content Comparing Decimal Tenth and Hundredth
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## Comparing Decimals – Tenth and Hundredth

What is comparing decimals? When comparing decimals tenths and hundredths, use the greater than, less than or equal to symbols.

In this text on comparing decimals, we practise comparing decimals with models in addition to looking at place value, because base ten blocks help us visualise 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
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.
• 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 practised yet? On this website you can find more interactive exercises, worksheets and more activities on comparing decimals to the tenths and hundredths.

## Comparing Decimal Tenth and Hundredth exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Comparing Decimal Tenth and Hundredth.
• ### Where do we start comparing?

Hints

We read numbers from left to right. Which place value do we look at first?

Ones are greater than tenths, and tenths are greater than hundredths.

Solution

We start comparing in the greatest place value.

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. Here we can see that 8 is greater than 2, therefore 0.25 < 0.8.

• ### Can you match the base ten models and decimals?

Hints

Look at the number in the tenths column. There should be that many full rows shaded in.

For example, 0.76 has a 7 in the tenths column so there are 7 full rows shaded plus 6 more individual squares.

A model that is entirely shaded in, represents one whole.

Remember, a decimal is part of a whole.

Solution
• 0.27 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 in 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. 0.15 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.
• ### Which decimals are greater than 0.74?

Hints

Greater than means bigger or larger.

Start to compare in the greatest place value.

For example, 0.25 and 0.8 both have 0 in the ones place so we move onto the tenths place where we can see that 2 < 8, therefore 0.25 < 0.8.

Grab some paper and a pencil and draw base ten models of each decimal and compare it to the model for 0.74.

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.

Solution

In 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 decimals greater than 0.74 are:

• 0.8
• 0.77
• 1.74
• 0.97
_______________________________________________________

• 0.64 is less than 0.74
• 0.74 is equal to 0.74
• ### Which is the correct symbol?

Hints

Start comparing by looking at the digit in the greatest place value.

Remember, all decimals must go to the same place. Use zero as a place holder if they do not go to the same place.

For example, 1.54 < 1.65.

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.

Solution

• 0.63 > 0.51 because 6 tenths is more than 5 tenths.
• 1.4 = 1.40 because 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.
• ### Compare the decimals using models.

Hints

Start with the greatest place value and compare. If the digits are the same, move on until the digits are different.

For example:

• Start by comparing the ones place.
• They have the same digit, so we move to the tenths place.
• They 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.

Remember, when decimals don't go to the same place, add a 0 as a place holder and then compare.

Solution
• 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; comparing the digits in the tenths place, we can see that 6 > 3 therefore 0.68 > 0.32.
• ### Greater than, less than, or equal to 1.2?

Hints

Remember, you are comparing each decimal to 1.2. Look at the decimal and compare the place values to 1.2. Draw models to help you if necessary.