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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