Session 3: Comparing Decimals – Steps, Interactive and Examples

What are Decimals?

Whole numbers are the set of numbers {0,1,2,3,…} that are non-negative and contain no fractional parts.

Not all numbers are whole numbers. The decimal system lets us represent numbers that are less than one and other numbers that exist between whole numbers. In a decimal number, the decimal point divides the whole part of the number from the decimal part of the number. Digits to the left of the decimal point represent whole numbers. Digits to the right of the decimal point represent decimal parts.

Here is an example.

45.237 is a decimal number between 45 and 46. The digits to the left of the decimal point are 45, so 45 is the whole number. The digits to the right of the decimal point are 237, so .237 is the decimal part.

Comparing Decimal Numbers

The value of each digit in a decimal number depends on its placement within the number. This concept is called place value. 

When comparing decimal numbers, keep two things in mind. First, compare the whole number parts, if they are greater than or lesser than the other number. The decimal having the greater whole number part is greater. Second, if the whole number parts are equal to each other, compare the tenth digits. We repeat this process and compare digits by working from left to right until we get the unequal digits.

1) Compare 56.983 and 56.99.

First, write the numbers in a place value chart. Make sure to line up the decimal points.

For these numbers, we first compare the whole number part. Both numbers have 56. So we need to move on to the number in tenth place.

When we look at the number in tenth place for 56.983 and 56.99, they are both 9.

So, now we compare the hundredth place. When we look at 56.983 and 56.99, the 9 in the hundredth place is larger than the 8.

∴ 56.99 is greater than 56.983.

Steps to Compare Decimal Numbers

To compare decimal numbers, we use the following steps:

Step 1: Obtain the decimal numbers.

Step 2: Compare the whole parts of the numbers. The number with the greater whole part will be greater. If the whole parts are equal, go to the next step.

Step 3: Compare the extreme left digits of the decimal parts of two numbers. The number with a greater extreme left digit will be greater. If the extreme left digits of decimal parts are equal, then compare the next digit and so on.

Ordering Decimal Numbers

We can use the same strategy to order decimal numbers from least to greatest.

Here is an example.

2) Arrange the decimals in descending order.

7.84, 3.16, 3.1 and 7.8

Converting the given decimals into like decimals, we get

7.84, 3.16, 3.10 and 7.80

Now, write the numbers in a place value chart. Make sure to line up the decimal points.

First, we need to find the number with the greatest value. We look at the number in the one’s place. There is a 7 in 7.84 and 7.80.

Then we look at the digits in the tenth place for 7.84 and 7.80. They are both 8.

Now we compare the digits in the hundredth place. When we look at 7.84 and 7.80, the 4 in the hundredth place is larger than the 0.

Our first two numbers in descending order are 7.84 and then 7.8.

Let’s look at 3.16 and 3.10. They both have a 3 in the ones place, so we move on to the tenth place.

There is a 1 in the tenth place for both numbers so let’s look at the hundredth place. In the hundredth place, there is a 6 and a 0. The number with the 6 in the hundredth place is greater: 3.16 is greater than 3.1.

Our numbers in descending order are:

7.84>7.8>3.16>3.1

Comparing Decimals – Examples

Example 1

Compare 0.046 and 0.048 using the place value chart.

Let us first write the numbers in a place value chart. Make sure to line up the decimal points.

Here the whole number parts are equal, so we compare the decimal parts. In decimal parts also digits up to hundredths place are equal. So, compare the digits at thousandths place. The digits at thousandths place are 6 and 8 respectively.

6<8
∴0.046<0.048

Example 2

Compare 5.823 and 5.82. 

Converting the given decimals into like decimals, we get

5.823 and 5.820

Here the whole number parts are equal, so we compare the decimal parts. In decimal parts also digits up to hundredths place are equal. So, compare the digits at thousandths place. The digits at thousandths place are 3 and 0 respectively. 

0<3
∴5.82<5.823

Example 3

Arrange the decimals in ascending order

6.53, 3.43, 4.04, 0.168 and 9.21

Converting the given decimals into like decimals, we get

6.530, 3.430, 4.040, 0.168 and 9.210    

Clearly, 

0.168<3.430<4.040<6.530<9.210

Hence, the given numbers in ascending order are:

0.168<3.43<4.04<6.53<9.21

Remember this!

To compare decimal numbers: Step 1: Obtain the decimal numbers.  Step 2: Compare the whole parts of the numbers. The number with the greater whole part will be greater. If the whole parts are equal, go to the next step.  Step 3: Compare the extreme left digits of the decimal parts of two numbers. The number with a greater extreme left digit will be greater. If the extreme left digits of decimal parts are equal, then compare the next digit and so on.