# 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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