Comparison of Decimals

In this section we will discuss comparison of decimals.



While comparing two decimal numbers:

1) The decimal fraction with the greater integral part will be greater.

2) If the integral parts of two decimal fractions are the same, then beginning from the tenths place the decimal fraction with the greater digit in the same place is greater.

1) Example Compare 0.62 or 0.071

Solution :

The integral parts of both the numbers are 0.

Now compare the next digits, 6 >0

So 0.62 > 0.071

2) Example : Compare 2.589 and 2.525

Solution :

The integral parts of both the numbers are 2.

The tenth digit of both numbers is also same.(5)

Now compare next digit, 8 > 2

So 2.589 > 2.525.

Arranging the decimal numbers in ascending/descending order :

3) Example :

Arrange 323.3, 3.323, 3.233, 3.332 and 33.23 in ascending order.

Solution:

First write all the decimals in place-value chart.

Decimals Hundreds Tens Ones Decimal point Tenths Hundredths Thousandths
323.3
3
2
3
.
3
0
0
3.323
3
.
3
2
3
3.233
3
.
2
3
3
3.332
3
.
3
3
2
33.23
3
3
.
2
3
0

The greatest integral part is 323, followed by 33,after which there are 3 decimals with the same integral part.

Here,3.233 is the smallest decimal as the digit in its tenths place is the smallest in this case.

323.3>33.23>3.332>3.323>3.233

Thus the decimals in descending order are

323.3,33.23,3.332,3.323,3.233
Practice

Q. 1 Put the proper sign.
1) 4.65 ( ) 4.56
2) 14.5 ( ) 18.56
3) 10 ( ) 1.56
4) 413.846 ( ) 413.384
5) 12.5678 ( ) 12.5677
Introduction of Decimals

• Expansion of decimals
• Comparison of decimals
• Addition of Decimals
• Subtraction of Decimals
• Multiplication of Decimals
• Division of Decimals
• Conversion of decimals to fraction

From comparison of decimals to Introduction of decimals

Number System

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