# Comparison of Decimal Fractions

This topic would deal with comparing decimal fractions.
For comparing decimal fractions we first compare the whole number part then
compare the fractional part. For comparing the fractional part we first compare
the tenths place, then hundredths place, then thousandths place and so on.

**For example:**

Compare 0.55 and 0.58

We cannot compare the
whole number part as both are same

We are comparing the
fractional decimal part

0.55 = 5 tenths + 5
hundredths

0.58 = 5 tenths + 8
hundredths

Now 5 tenths = 5 tenths

We will now compare next
place

5 hundredths < 8
hundredths

Steps of comparing decimal
fractions:

**Step I:** First compare the whole
number part.

Then if the whole number
part of both the numbers are same then compare the tenths place.

**Step II:** If the tenths place is same
or equal then compare the hundredths place.

**Step III:** If the hundredths place is
same or equal then compare the thousandths place and so on.

**Here are few examples of
comparing decimal fractions:**

**1. Compare 45.63 and 45. 976**

45.63 = 4 tens + 5 ones
+ 6 tenths + 3 hundredths

45.976 = 4 tens + 5 ones
+ 9 tenths + 7 hundredths + 6 thousandths

4 tens = 4 tens

5 ones = 5 ones

6 tenths < 9 tenths

Therefore, 45.63 <
45.976

**2. Which is greater 90.678
or 65.321?**

90.678 = 9 tens + 0 ones
+ 6 tenths + 7 hundredths + 8 thousandths

65.321 = 6 tens + 5 ones
+ 3 tenths + 2 hundredths + 1 thousandths

Now we see,

9 tens > 6 tens

Hence 90.678 >65.321

**3. Compare 45.213 and 785.
563**

45.213 = 4 tens + 5 ones
+ 2 tenths + 1 hundredths + 3 thousandths

785.563 = 7 hundreds + 8
tens + 5 ones + 5 tenths + 6 hundredths + 3 thousandths

Now we will first
compare the integral part

4 tens < 7 hundreds

Therefore, 45.213 <
785.563

**4. Which is greater 32.124
or 32.128**

32.124 = 3 tens + 2 ones
+ 1 tenths + 2 hundredths + 4 thousandths

32.128 = 3 tens + 2 ones
+ 1 tenths + 2 hundredths + 8 thousandths

Now we will first
compare the integral part

3 tens = 3 tens

2 ones = 2 ones

Now we will compare the decimal fraction part

1 tenths = 1 tenths

2 hundredths = 2
hundredths

4 thousandths < 8
thousandths

Therefore, 32.124 <
32.128

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