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comPariNg aND orDeriNg Decimals

We know that a decimal number contains two parts: whole number part and decimal part.
So, we compare the whole number part first and then the decimal part.

To compare two decimal numbers, we follow the following steps:
Step 1: First convert all decimal numbers into like decimals.

Step 2: Compare the whole number part first; the decimal number with greater whole
number part will be greater.
Step 3: If the whole number parts are equal, then compare their decimal parts.

Step 4: Start comparing from the tenths place. The number with the greater digit in the
tenths place will be greater.
Step 5: If tenths place digits are equal, then compare hundredths place digit. Decimal
number with greater hundredths place digit will be greater.

Step 6: If hundredths place digits are same, then follow the similar process to compare
thousandths place, ten thousandths place and so on.
example 1: Compare 8.64 and 13.29. 8 • 64 13 • 29

Solution: 8.64 and 13.29 are like decimals.
Comparing the whole number part, we observe that 8 < 13.

Thus, 8.64 < 13.29.
example 2: Compare 38.26 and 38.9.

Solution: 38.26 and 38.9 are unlike decimals. t O • t h

So, converting the unlike decimals into like decimals, we 3 8 • 2 6
get 38.26 and 38.90. 3 8 • 9 0
Now, since whole number parts of both the decimals Same 2 < 9
are equal, we compare decimal parts.

Here, 2 tenths < 9 tenths.
So, 38.26 < 38.90.

example 3: Which is smaller: 0.643 or 0.61? O • t h th
Solution: 0.643 and 0.61 are unlike decimals. 0 • 6 4 3

So, converting them into like decimals, we get 0.643 and
0.610. 0 • 6 1 0
Here, whole number parts are equal, so we compare Same 4 > 1
the decimal parts. Here, tenths place digits are same, i.e., 6 = 6.

So, compare hundredths place digits.
Here, 4 hundredths > 1 hundredth.

So, 0.643 > 0.610
Thus, 0.61 < 0.643

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