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Comparison Of Decimal Numbers

Comparison of Decimal Numbers

  • If there are two decimal numbers we can always compare them. One of the numbers will either be greater than, less than or equal to the other.
  • For comparison of two decimal numbers, firstly, compare the wholes of both the numbers.

Case 1: If the wholes are not same:

If the wholes of the two decimal numbers are not same, then the decimal number with larger wholes is greater than the other.

For example: We want to compare two decimal numbers, \(60.8\) and \(45.5\)

  • In the first step, we compare the wholes of both the numbers.

  • On comparing, we observe that both the wholes are different.

\(\because\;60\) is greater than \(45\).

\(\therefore\) Decimal number \(60.8\) is greater than \(45.5\)

\(60.8>45.5\)

Case 2: If the wholes are same:

  • If the wholes of the two decimal numbers are same, but the parts are different, then the decimal number with larger parts is greater than the other one.

For example: We want to compare two decimal numbers, \(0.90\) and \(0.77\)

  • Here, wholes are same i.e., \('0'\).
  • So, ignore the decimal point and compare as whole numbers.

\(\because\;90\) is greater than \(77\)

\(\therefore\) Decimal number \(0.90\) is greater than \(0.77\)

\(0.90>0.77\)

Illustration Questions

Which one of the following options shows the correct comparison between \(2.80\) and \(2.90\) ?

A \(2.80>2.90\)

B \(2.80\geq2.90\)

C \(2.80=2.90\)

D \(2.80<2.90\)

×

Firstly, we compare the wholes of both the numbers.

On comparing, we observe that both the wholes are same.

image

Now, we have to compare the parts of both the numbers.

image

On comparing we observe that,

\(\because\;80\) is less than \(90\)

\(\therefore\) Decimal number \(2.80\) is less than \(2.90\)

Thus, \(2.80<2.90\)

Hence, option (D) is correct.

Which one of the following options shows the correct comparison between \(2.80\) and \(2.90\) ?

A

\(2.80>2.90\)

.

B

\(2.80\geq2.90\)

C

\(2.80=2.90\)

D

\(2.80<2.90\)

Option D is Correct

Ordering Decimals

  • Ordering means to form a series of decimals according to their value.
  • We can arrange them from least to greatest or from greatest to least.

Example: \((a<b<c<d)\) or \((a>b>c>d)\)

  • For ordering decimals according to their values, compare the given decimal numbers with each other and then arrange from least to greatest or from greatest to least.

For example: We want to arrange the three decimal numbers, \(0.23,\;0.45\) and \(0.12\) in increasing order.

 

 First, we compare the wholes of the given numbers.

On comparing, we observe that all the wholes are same.

Now, we compare parts of the given numbers.

On comparing, we observe that all the parts are different.

Here, \(23\) is smaller than \(45\) and greater than \(12.\)

This can be arranged as

\(12<23<45\)

Therefore, \(0.12<0.23<0.45\)

Illustration Questions

Arrange \(1.35,\;1.25,\;1.85\) and \(1.65\) in ascending order.

A \(1.35,\;1.25,\;1.85,\;1.65\)

B \(1.85,\;1.65,\;1.35,\;1.25\)

C \(1.25,\;1.35,\;1.85,\;1.65\)

D \(1.25,\;1.35,\;1.65,\;1.85\)

×

First, we compare the wholes of the given numbers.

On comparing, we observe that all the wholes are same.

image

Now, we compare parts of the given numbers.

On comparing, we observe that all the parts are different.

image

Here, \(35\) is greater than \(25\) but less than \(65\) and \(85\).

\(65\) is less than \(85\).

Arranging the numbers in ascending order(from least to greatest number), i.e

\(25<35<65<85\)

\(\therefore\;1.25<1.35<1.65<1.85\)

Hence, option (D) is correct.

Arrange \(1.35,\;1.25,\;1.85\) and \(1.65\) in ascending order.

A

\(1.35,\;1.25,\;1.85,\;1.65\)

.

B

\(1.85,\;1.65,\;1.35,\;1.25\)

C

\(1.25,\;1.35,\;1.85,\;1.65\)

D

\(1.25,\;1.35,\;1.65,\;1.85\)

Option D is Correct

Ordering of Decimals

  • Ordering means to form a series of decimals according to their value.
  • We can arrange them from least to greatest or from greatest to least.

Example: \((a<b<c<d)\) or \((a>b>c>d)\)

  • For ordering decimals according to their values, compare the given decimal numbers with each other and then arrange from least to greatest or from greatest to least.

For example: We want to arrange the three decimal numbers, \(9.6,\;9.85\) and \(9.575\) in ascending order.

  • For arranging the numbers in order from least to greatest.
  • First, make all the decimal numbers to have the same place values.

\(9.6\) can be written as \(9.600\)

\(9.85\) can be written as \(9.850\)

  • Now, all the decimal numbers have the same place values.

\(9.600,\;9.850,\;9.575\) 

 Now, compare the wholes of numbers.

 On comparing, we observe that all the wholes are same.

Now, we compare the parts of the given numbers.

On comparing, we observe that all the parts are different.

Here, \(600\) is greater than \(575\) and less than \(850\).

Arranging the decimal number in ascending order(from least to greatest), i.e.

\(575<600<850\)

\(\therefore\;9.575<9.600<9.850\)

or \(9.575,\;9.6,\;9.85\)

Illustration Questions

Arrange \(15.5,\;15.6,\;15.05\) and \(15.550\) in ascending order.

A \(15.5<15.6<15.05<15.550\)

B \(15.05>15.550>15.5>15.6\)

C \(15.05<15.5<15.550<15.6\)

D \(15.6<15.550<15.5<15.05\)

×

For arranging the numbers in ascending order,

first, make all the decimal numbers to have the same place values.

\(15.5\) can be written as \(15.500\)

\(15.6\) can be written as \(15.600\)

\(15.05\) can be written as \(15.050\)

Now, all the decimal numbers have the same place values.

\(15.500,\;15.600,\;15.050,\;15.550\)

Now, we compare the wholes of the given numbers.

On comparing, we can clearly see that all the wholes are same.

image

Now, we compare the parts of the given numbers.

On comparing, we observe that all the parts are different.

image

Here, \(500\) is greater than \(050\) but less than \(550\) and \(600\) is greater than \(550\).

Arranging the decimal number in ascending order(from least to greatest), i.e.

\(050<500<550<600\)

\(\therefore\;15.05<15.5<15.550<15.6\)

Hence, option (C) is correct.

Arrange \(15.5,\;15.6,\;15.05\) and \(15.550\) in ascending order.

A

\(15.5<15.6<15.05<15.550\)

.

B

\(15.05>15.550>15.5>15.6\)

C

\(15.05<15.5<15.550<15.6\)

D

\(15.6<15.550<15.5<15.05\)

Option C is Correct

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