Comparing Decimals

Comparing decimals means finding out the larger and the smaller decimal number in a given set of numbers. Decimal numbers can be compared in the same way as we compare other numbers. However, we need to remember that the digits that are placed after the decimal point also need to be considered. These digits have place values starting from tenths, followed by hundredths, then thousandths, and so on. Let us learn more about comparing decimals in this article.

Comparing decimals is similar to comparing other whole numbers in which we start comparing the digits with the greatest place value. We place the given decimal numbers in a place value chart and start the comparison. If the digits on the greatest place value are the same, we move on to the digits in the next place to the right. We keep comparing digits until we reach the digits that are different. Let us understand this with the help of the following example.

Example: Compare 0.64 and 0.362

Solution:

• Step 1: Compare the whole number part, which is the ones digit. If the numbers are the same, go to the next step. In this case, the ones digits has 0 in both the numbers. So, we move on to the next place to the right.
• Step 2: Compare the tenths place, which is the place to the right of the decimal point. When we compare the value in the tenths place, we see that 6 is greater than 3. At this step itself, we get to know that 0.64 is greater than 0.362. Therefore, we do not need to move on to the hundredths digit for further comparison.
• Step 3: Hence, we conclude that 0.64 > 0.362

When we need to compare decimals and fractions, we first convert the given fraction to a decimal number and then compare the numbers using the same procedure.

Example: Compare 3/4 and 0.728

Solution: First, let us convert 3/4 to a decimal number by dividing 3 by 4. So, 3 ÷ 4 = 0.75. Now, we have both the numbers in the decimal form. So, let us compare 0.75 and 0.728 using the method given above.

• Step 1: Compare the whole number part, which is the ones digit. In this case, the ones digits has 0 in both the numbers. So, we will move on to the next place value to the right.
• Step 2: Compare the tenths place, which is the first place to the right of the decimal point. When we compare the value on the tenths digit, we see that both the numbers have 7. So we move on to the hundredths place.
• Step 3: Compare the hundredths place. Now, when we compare the value at the hundredths place, we see that 5 is greater than 2. At this step, we get to know that 0.75 is greater than 0.728. Therefore, we do not need to move on to the thousandths digit for further comparison.
• Step 3: Hence, we conclude that 0.75 > 0.728 which means 3/4 > 0.728

When we compare decimals on a number line, we follow the basic rule of the number line which says that, as we move to the right the value of the numbers increases. For example, if we need to compare 6.5 and 6.7, we mark the decimal numbers on the number line in such a way that both the numbers are included.

We need to focus between 6 and 7 because both the given numbers lie between 6 and 7. We mark 6 at the left end and 7 at the right end. Then, we mark all the numbers in between, to scale, writing 6.5 midway between 6 and 7. After marking the other tenths, we see that 6.7 comes to the right side of 6.5, therefore 6.5 < 6.7. Hence, it be concluded that 6.5 < 6.7 because 6.7 comes to the right of 6.5 on the number line.

We have already seen that we compare decimal numbers starting from the whole number part and then we move on to the digits given after the decimal point. Let us see how to compare decimals to the hundredths place.

Example: Compare 8.362 and 8.391 to find the greater number.

Solution: Let us follow the same steps as shown above.

• Step 1: Compare the whole number part. In this case, the whole number part has 8 in both the numbers. So, we will move on to the next place value.
• Step 2: Compare the tenths place, which is the first place to the right of the decimal point. When we compare the value on the tenths digit, we see that both the numbers have 3. At this point, we move on to the hundredths place.
• Step 3: Compare the hundredths place. Now, when we compare the value at the hundredths place, we see that 9 is greater than 6. So, we get to know that 8.391 is greater than 8.362. Therefore, we do not need to move on to the thousandths digit for further comparison.
• Step 3: Hence, we conclude that 8.362 < 8.391

Related Links

Check out the following pages related to comparing decimals.

• Decimals
• Decimals and Fractions
• Adding Decimals

How do you Compare Decimals?

Decimals are compared in the same way as we compare other whole numbers. The only point to be remembered is that we also need to consider the place values given after the decimal point. These place values start with tenths, followed by hundredths and thousandths, and so on. First, we compare the digits before the decimal point. If these digits are equal, then we move on to compare the digits after the decimal. If they are unequal, the comparison is done at that step itself and we don't move further for any comparison. In other words, we keep comparing the digits to the right until we get a set of unequal digits to compare.

What are the Rules for Comparing Decimals?

There are certain rules for comparing decimals. Let us understand them with the help of the following example. For example, let us compare 5.274 and 5.237

• Step 1: First, compare the whole number part. If the numbers are the same, go to the next step. In this case, the whole number part (the ones digit) has 5 in both the numbers. So, we move on to the next place value to the right.
• Step 2: Compare the tenths place, which is the digit to the right of the decimal point. When we compare the value on the tenths digit, we see that both the numbers have 2. So, we again move on to the next place value which is the hundredths place.
• Step 3: Compare the hundredths place. Now, when we compare the value at the hundredths place, we see that 7 is greater than 3. At this step itself, we get to know that 5.274 is greater than 5.237. Therefore, we do not need to move on to the thousandths digit for further comparison.
• Step 3: Hence, we conclude that 5.274 > 5.237

How to Compare Decimals and Fractions?

When we need to compare decimals and fractions, we first convert the given fraction to a decimal number and then compare them using the same procedure. For example, let us compare 0.528 and 3/7. In this case, we will convert 3/7 to a decimal number by dividing 3 by 7. So, 3 ÷ 7 = 0.428. Now, we can compare 0.428 and 0.528 because both the numbers are in the decimal form. So, we start the comparison from the whole number part, which is 0 in both the numbers. So, we move on to the tenths digit which is different in both the numbers. At this step, we can say that 0.528 is greater than 0.428. We do not need to go to the next digit for any further comparison. Hence 3/7 < 0.528.

How to Compare Decimals from Least to Greatest?

Comparing decimals from least to greatest means arranging them in ascending order in which the smallest number comes first, followed by the greater numbers. For example, let us compare a given set of numbers from least to greatest. The given numbers are 1.002, 0.112, 1.102. We will start the comparison from the largest place value, which is ones in this case. So, we can see that 0.112 has the least value in ones place, which means this is the smallest number in all, therefore, we will place it first. Now, we will compare the remaining two numbers, 1.002 and 1.102, in which the ones place is equal. So, we compare the tenths place which is 0 and 1 in the respective numbers. This shows that 1.002 is the smaller number. So, we will place it as the next number in the list, followed by 1.102. Hence, the given numbers can be arranged from least to greatest as, 0.112, 1.002, 1.102.

How to Compare Decimals on a Number Line?

When we compare decimals on a number line, we follow the basic rule of the number line which says that, as we move to the right, the value of the numbers increases. For example, if we need to compare 4.3 and 4.7, we mark the decimal numbers on the number line in such a way that both the numbers are included. We see that 4.7 comes to the right of 4.3. Therefore, 4.7 is greater than 4.3

How to Compare Decimals to Hundredths Place?

We compare decimals to the hundredths place when we have checked all the place values before it, that is, the whole number part, and the tenths place. If the numbers in these places are equal, we come to the hundredths place for comparing the numbers. Let us understand this with an example. Let us compare 7.14 and 7.16

• Step 1: First, let us compare the whole number part. In this case, the whole number part has 7 in both the numbers. So, we will move on to the next place value.
• Step 2: Now, when we compare the tenths place, which is the first place to the right of the decimal point, we find that both the numbers have 1. At this point, we move on to the hundredths place.
• Step 3: We compare the hundredths place and see that 6 is greater than 4. So, we get to know that 7.16 is greater than 7.14.
• Step 3: Hence, we conclude that 7.16 > 7.14

How to Compare Decimals to Thousandths Place?

Comparing decimals to thousandths place is similar to the comparison to hundredths place. In this case, when we have compared the numbers up to the place of the hundredths digit, and we find that both the numbers are equal, we come to the thousandths place for the comparison. On this place, if the digits are different, we can compare the numbers and get to know the larger number.