METHOD OF COMPARING DECIMALS EXPLAINED LUCIDLY WITH EXAMPLES AND EXERCISES

Please study Decimals before Comparing decimals,
if you have not already done so.

The knowledge of decimals and

Decimal Place value chart are prerequisites here.

To know the order relation in decimals
is relatively easier compared to that in
vulgar Fractions.

There, we have to find the L.C.M. of the denominators
of the given set of fractions and convert them into
equivalent fractions using that L.C.M. to compare.



Here the following Note is made use of.
Note :

putting any number of zeroes to the extreme right
side of the decimal part of a decimal does
not change the value of the decimal.

Method of Comparing decimals

Step 1 :
First compare the whole number parts.
The decimal with greater whole number is greater.

Step 2 :
Make the number of digits after the decimal
point equal by putting zeroes to the extreme
right side of the decimal part, if required.

Step 3 :
If the whole number parts are equal,
compare the tenths digits. The decimal with the
bigger digit in the tenths place is greater.

Step 4 :
If the tenths digits are equal, compare
the hundredths digits, and so on.

Example 1 of Comparing decimals

Compare 51.42 and 49.79

Solution:
The given decimals are 51.42 and 49.79.
First, let us compare the whole number parts.
Obviously, 51 > 49.
∴ 51.42 > 49.79. Ans.

Example 2 of Comparing decimals

Compare 83.8 and 83.59

Solution:
here, the whole number part of
the given decimals is same.

The given decimals are 83.8 and 83.59
or 83.80 and 83.59.

Comparing the tenths' digits,
obviously, 8 > 5.

∴83.80 > 83.59 or 83.8 > 83.59. Ans.

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Example 3 of Comparing decimals

Write the following decimals in ascending order.
16.01, 7.23, 0.9, 0.965, 1.001.

Solution:
Here, the whole numbers are 16, 7, 0, 0, 1.
In ascending order they are 0, 0, 1, 7, 16.
The two decimals with whole number part 0,
are 0.9 and 0.965 or 0.900 and 0.965.
Here, the digits in the tenths place are equal.
The digits in the hundredths place are 0 and 6.
Obviously, 0 < 6.
∴0.900 < 0.965.

Hence, the given decimals in ascending order are
0.9, 0.965, 1.001, 7.23, 16.01. Ans.

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Example 4 of Comparing decimals

Write the following decimals in descending order.
99.9, 0.9, 9.9, 0.09, 9.09. 9.99

Solution:
Here, the whole numbers are 99, 0, 9
In descending order they are 99, 9, 0.
So, the decimal with 99 as whole number is the largest,
followed by those with whole number 9 and then with 0.

The decimals with 9 as whole number
are 9.9, 9.09, 9.99 or 9.90, 9.09, 9.99
Comparing tenths' digits,
9.09 is less than the other two as 0 < 9.
Comparing hundredths' digits,
9.99 > 9.90 as 9 > 0.
Thus, 9.99 > 9.90 > 9.09.

The decimals with 0 as whole number
are 0.9, 0.09 or 0.90, 0.09
Comparing tenths' digits, 0.90 > 0.09, as 9 > 0.

Hence, the given decimals in descending order are
99.9 > 9.99 > 9.90 > 9.09 > 0.90 > 0.09. Ans.

Exercise on comparing decimals

1. Fill in the blank with > or <
   1. 17.93 --- 16.99
   2. 1.708 --- 1.78
   3. 34.78 --- 34.87
   4. 3.09 --- 3.009
   5. .99 --- 1
2. Arrange the following decimals in ascending order :
   1. 1.6, 2.2, 1.57, 2.18, 1.18, 2.08
   2. 0.8, 0.008, 0.08, 8.8, 8.08, 0.88
3. Arrange the following decimals in descending order :
   1. 3.3, 0.03, 0.3, 0.003, 3.33, 33.3
   2. 4.9, 5.6, 9.2, 8.3, 5.06, 8.03

For Answers see at the bottom of the page.

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Answers to Exercise on comparing decimals

1.  
   1. 17.93 > 16.99
   2. 1.708 < 1.78
   3. 34.78 < 34.87
   4. 3.09 > 3.009
   5. .99 < 1
2.  
   1. 1.18, 1.57, 1.6, 2.08, 2.18, 2.2
   2. 0.008, 0.08, 0.8, 0.88, 8.08, 8.8,
3.  
   1. 33.3, 3.33, 3.3, 0.3, 0.03, 0.003
   2. 9.2, 8.3, 8.03, 5.6, 5.06, 4.9

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