In this post we will learn about comparison of decimals.

After learning the concept we will move on to solve questions related to the above topic.

Understand that these topics comes under Saxon Grade 5 Math Curriculum and it sets the base for higher math topics.

**How to compare two decimal numbers?**

We will understand two method of decimal comparison

Method 1 : Simple Decimal Comparison

Method 2: Decimal Comparison using Place Value Chart

**Method 01 : Simple Decimal Comparison**

In order to compare the given decimals we have to make sure that every given decimals have same digits.

For Example;

Consider the below decimal numbers

In the above example:

0.36 ⟹ has two decimal place value

0.421⟹ has three decimal place value

make sure all numbers have same decimal place.

This can be done by **inserting 0 at the end of digits with less decimal place**

Now both the numbers have same place value.

Compare both the decimals as we compare the whole numbers

We know that; 360 < 421

Its decimal equivalent will also be the same; 0.360 < 0.421

**Hence, 0.360 < 0.421 is the final answer**

**Method 2 : Number comparison using Place Value chart**

**Step 01**

Fill up the place value chart with the given number

Also fill up the empty boxes with 0

**Step 02**

Start comparing numbers from left corner**(a) Comparing Ones Place Value**

Both numbers have 0, so can’t make any decision.

Let’s move on to Tenths Place value

**(b) Comparing Tenth Place Value**

Observe that 3 < 4

From this we can conclude that 0.360 < 0.421

No need to do further analysis.

**Example 02**

Compare the decimals 0.32, 0.4, 0.671

**Method 01: Simple Decimal Comparison**

**Step 01**

Find decimal place value of all numbers

**Step 02**

Convert all the number to highest decimal place by inserting 0

Observe that 0.671 has three decimal place (highest)

So transform all the number into three decimal place number

**Step 03**

Compare all the decimal number

we know that

671 > 400 > 320

The same will be true for decimal number**0.671 > 0. 400 > 0.230**

Hence the above order is the solution of the problem

**Method 2: Comparison using Place Value Chart**

Start comparing numbers from left to right

**Step 01: Compare ones value**

All numbers are 0 hence can’t decide

**Step 02: Compare Tenth Value**

From the table we figure out that: 6 > 4 > 3

So we conclude the right order of decimal is **0.671 > 0.400 > 230**

Let us see another example of decimal with whole number

**Example 03**

Compare the below decimals and arrange them in descending order

0.52, 1.56, 0.434

**Method 01: Simple Decimal Comparison****Step 01**

Make sure all the numbers have same number of decimal place

0.434 has 3 decimal place value

Ensure all the number have 3 decimal place value

**Step 02**

Compare the whole numbers (if present)

Only 1.560 contains the whole number, so it is the largest number among the three.

Now compare the other two numbers (0.520 & 0.434)

**Step 03**

Compare the numbers after decimal

We will compare number after decimals just like whole number

Since, 520 > 434

We conclude 0.520 > 0.434

Hence the final order will be ⟹ **1.56 > 0.52 > 0.436**

**Method 2 : Decimal comparison using Place Value Chart****Step 01**

Fit all the numbers in place value and put 0 in the empty spaces

**Step 02**

Start comparing numbers from left to right

**(a) Comparing Ones Values**

Two numbers have digit 0’s

One number have digit 1

Since, 1 > 0;

The number with digit 1 is largest among the other two

From the above table we can conclude that:

1.560 > 0.520 & 0.434

Now compare the rest of the numbers (0.520 & 0.434)

**(b) Compare tenth value**

In Tenth Place value, digit 5 (of 0.520) is greater than digit 4 (0.434)

Hence 0.520 > 0.434

From the above deliberation we can conclude that:**1.560 > 0.520 > 0.434**

Let us look at one final example

**Example 04**

Compare the below decimals and arrange them in descending order

1.25, 2.442, 1.247

**Method 01: Simple Decimal Comparison**

Make sure all the numbers have same decimal place

⟹ 2.442 & 1.247 has three decimal place

⟹ We have to insert one zero to number 1.25

**Step 02**

Compare the whole numbers (if present)

Since whole number 2 is greatest among all the digits present.

We conclude that 2.442 is greater than both 1.250 & 1.247

i.e. 2.442 > 1.250 & 1.247

Let us compare the other two numbers (1.250 & 1.247)

**Step 03**

Compare the numbers after decimals

Compare both the decimals just as a whole number

As 250 > 247, we conclude 1.250 > 1.247

Hence the order of number is**2.442 > 1.250 > 1.247**

**Method 2: Using Place Value Chart**

**Step 01**

Fill up the numbers in place value and put 0 in empty spaces

**Step 02**

Start comparing numbers from left to right

**(a) compare digits in Ones Place**

Note that digit 2 is the largest among all the three.

hence 2.442 > 1.247 & 1.250

**(b) Compare digits in Tenth Place**

Since both digits are same (digit 2), we can’t come to any conclusion.

Move on to compare digits at hundredth place

**(c) Compare digits in Hundredth Place**

Since 5 > 4;

we conclude that 1.250 > 1.247

Hence the final arrangement of number is 2.442 > 1.250 > 1.247

Now we have understood the concept, it is now time to solve some related problems

**Decimal Comparison Worksheet**

Given below are collection of questions related to ordering of decimals.

All the questions are to the standard of grade and are provided with detailed solution.

**Compare the given decimal numbers**

Two decimal numbers are given below.

Compare the two decimals and arrange them accordingly

(a) 4.252 and 4.24

Read SolutionUsing Decimal Place Value Chart and filling empty spaces with 0

Start comparing numbers from the left

(a) Comparing the Ones Place

Both contain digit 4, hence we can’t draw any conclusion

(b) Compare Tenths Place

Booth contain digit 2, again can’t conclude anything.

(c) Compare Hundredth Place

Digit 5 > Digit 4

Hence **4.252 > 4.240**

(b) 1.25 and 0.91

Read SolutionCompare the integer part of the given number

Integer for 1.25 ⟹ 1

Integer for 0.91 ⟹ 0

We know that 1 > 0

Hence **1.25 > 0.91**

(c) 21.256 and 21.270

Read SolutionInteger for 21.256 ⟹ 21

Integer for 21.270 ⟹ 21

Both integers are same.

We can’t conclude anything.

Step 02 : Compare the decimal number

Decimal for 21.256 ⟹ 0.256

Decimal for 21.270 ⟹ 0.270

we know that, 256 < 270

Similar can be said for decimals, 0.256 < 0.270

Hence **21.256 < 21.270**

(d) Compare 656.91 and 656.82

Read Solution**Step 01: Compare the integer numbers**

Integer for 656.91 ⟹ 656

Integer for 656.82 ⟹ 656

Both integers are same.

Cannot conclude anything

**Step 02: Compare the decimals**

Decimal for 656.91 ⟹ 0.91

Decimal for 656.82 ⟹ 0.82

We know that 91 > 82

Similar can be said for decimal equivalent, 0.91 > 0.82

Hence **656.91 > 656.82**

(e) Compare 143.042 and 143.42

Read SolutionFirst make sure both numbers have same decimal places

⟹ 143.042 & 143.420

**Step 01: Compare the integer numbers**

Integer for 143.042 ⟹ 143

Integer for 143.42 ⟹ 143

Both integers are same

Cannot conclude anything

**Step 02 : Compare the decimal numbers**

Decimal for 143.042 ⟹ .042

Decimal for 143.420 ⟹ .420

We know that 042 < 420

Similar is the case for its decimal equivalent .042 < .420

Hence 143.042 < 143.420

You can also solve this questions using Place Value Chart

(f) Compare 1424.69 and 1424.684

Read SolutionFirst make sure both numbers have same decimal places

⟹ 1424.690 & 1424.684

**Step 01: Compare the integer numbers**

Integer for 1424.690 ⟹ 1424

Integer for 1424.684 ⟹ 1424

Both integers are same

Cannot conclude anything

**Step 02 : Compare the decimal numbers**

Decimal for 1424.690 ⟹ .690

Decimal for 1424.684 ⟹ .684

We know that 690 < 684

Similar is the case for its decimal equivalent .690 < .684

Hence **1424.690 > 1424.684**

(g) Compare 544.64 and 450.92

Read Solution**Step 01: Compare the integer numbers**

Integer for 544.64 ⟹ 544

Integer for 450.92 ⟹ 450

Since 544 > 450

We conclude that 544.64 > 450.92

(h) **Compare 0.619 and 0.61**

First make sure both numbers have same decimal places

⟹ 0.619 & 0.610

**Step 01: Compare the integer numbers**

Integer for 0.619 ⟹ 0

Integer for 0.610 ⟹ 0

Both integers are same

Cannot conclude anything

**Step 02 : Compare the decimal numbers**

Decimal for 0.619 ⟹ .619

Decimal for 0.610 ⟹ .610

We know that 619 > 610

Similar is the case for its decimal equivalent 0.619 > 0.610

**Hence 0.619 > 0.610 is the solution**

(h) Compare 9.51 and 9.521

Read SolutionFirst make sure both numbers have same decimal places

⟹ 9.510 & 9.521

**Step 01: Compare the integer numbers**

Integer for 9.510 ⟹ 9

Integer for 9.521 ⟹ 9

Both integers are same

Cannot conclude anything

**Step 02 : Compare the decimal numbers**

Decimal for 9.510 ⟹ .510

Decimal for 9.521 ⟹ .521

We know that 510 < 521

Similar is the case for its decimal equivalent 0.510 < 0.521

Hence, **9.510 < 9.521 is the right answer**

(i) Compare the decimals 0.569 and 0.562

Read Solution**Step 01: Compare the integer numbers**

Integer for 0.569 ⟹ 0

Integer for 0.562 ⟹ 0

Both integers are same

Cannot conclude anything

**Step 02 : Compare the decimal numbers**

Decimal for 0.569 ⟹ .569

Decimal for 0.562 ⟹ .562

We know that 569 > 562

Similar is the case for its decimal equivalent 0.569 > 0.562

Hence, **0.569 > 0.562 is the right answer**

(j) Compare the decimals 0.01 and 0.001

Read SolutionFirst make sure both numbers have same decimal places

⟹ 0.010 & 0.001

**Step 01: Compare the integer numbers**

Integer for 0.010 ⟹ 0

Integer for 0.001 ⟹ 0

Both integers are same

Cannot conclude anything

**Step 02 : Compare the decimal numbers**

Decimal for 0.010 ⟹ .010

Decimal for 0.001 ⟹ .001

We know that whole numbers, 010 > 001

Similar is the case for its decimal equivalent 0.010 < 0.001

Hence, **0.010 > 0.001 is the right answer**

**Arrange the decimals in descending order**

Given below are four set of numbers.

You have to compare the decimals and arrange them in descending order

(a) Arrange the below decimals**2.54, 2.5, 2.05, 2.1**

Make sure all the decimals have same place value

2.54, 2.50, 2.05, 2.10

**Step 01: Compare the integer numbers**

Integer for 2.54 ⟹ 2

Integer for 2.50 ⟹ 2

Integer for 2.05 ⟹ 2

Integer for 2.10 ⟹ 2

All integers are same

Cannot conclude anything

**Step 02 : Compare the decimal numbers**

Decimal for 2.54 ⟹ 0.54

Decimal for 2.50 ⟹ 0.50

Decimal for 2.05 ⟹ 0.05

Decimal for 2.10 ⟹ 0.10

We know that whole numbers show following relationship

54 > 50 > 10 > 05

Similar will be the case for respective decimal numbers

0.54 > 0.50 > 0.10 > 0.05

Hence the final arrangement of number is :

2.54 > 2.50 > 2.10 > 2.05

(b) Arrange the below decimals in descending order**5.09, 5.42, 4.31, 4.22**

**Step 01: Compare the integer numbers**

Integer for 5.09 ⟹ 5

Integer for 5.42 ⟹ 5

Integer for 4.31 ⟹ 4

Integer for 4.22 ⟹ 4

Here we conclude that

5.09 & 5.42 are greater than numbers 4.31 & 4.22

**Step 02: Compare the decimal number of 4.31 & 4.22**

Decimal for 4.31 ⟹ 0.31

Decimal for 4.22 ⟹ 0.22

we know that 31 > 22

So the decimal equivalent be like 0.31 > 0.22

Hence **4.31 > 4.22** ——— eq(1)

**Step 03: Compare the decimal number of 5.09 & 5.42**

Decimal for 5.09 ⟹ 0.09

Decimal for 5.42 ⟹ 0.42

we know that 42 > 09

So the decimal equivalent will be 0.42 > 0.09

Hence **5.42 > 5.09** ——– eq(2)

From eq(1) & eq(2), we conclude that:**5.42 > 5.09 > 4.31 > 4.22**

(c) Arrange the decimals in descending orders**9.15, 4.25, 4.05, 8.67**

**Step 01: Compare the integer numbers**

Integer for 9.15 ⟹ 9

Integer for 4.25 ⟹ 4

Integer for 4.05 ⟹ 4

Integer for 8.67 ⟹ 8

We know that 9 > 8 > 4

Here we conclude that

9.15 > 8.67 > 4.05 & 4.25 —-eq (1)

We have to find which number is greater among 4.05 & 4.25

**Step 02: Compare the decimal number of 4.05 & 4.25**

Decimal for 4.05 ⟹ 0.05

Decimal for 4.25 ⟹ 0.25

we know that 05 < 25

So the decimal equivalent be like 0.05 < 0.25

Hence **4.05 < 4.25** ——— eq(2)

From eq(1) and eq(2), we get following solution:**9.15 > 8.67 > 4.25 > 4.05**

(d) Arrange the numbers in descending order**6.256, 1.554, 10.306, 4.321**

**Step 01: Compare the integer numbers**

Integer for 6.256 ⟹ 6

Integer for 1.554 ⟹ 1

Integer for 10.306 ⟹ 10

Integer for 4.321 ⟹ 4

we know that:

10 > 6 > 4 > 1

Hence the final arrangement will be :

10.306 > 6.256 > 4.321 > 1.554

(e) Arrange the decimals in descending orders**47.31, 47.91, 45.12, 44.19**

**Step 01: Compare the integer numbers**

Integer for 47.31 ⟹ 47

Integer for 47.91 ⟹ 47

Integer for 45.12 ⟹ 45

Integer for 44.19 ⟹ 44

We know that 47 > 45 > 44

Hence 47.31 & 47.91 > 45.12 > 44.19 — eq(1)

We have to find which number is greater among 47.31 & 47.91

**Step 02: Compare the decimal number of 47.31 & 47.91**

Decimal for 47.31 ⟹ 0.31

Decimal for 47.91 ⟹ 0.91

we know that whole number 91 > 31

Hence decimal equivalent will be the same 0.91 > 0.31

We conclude that 47.91 > 47.31 –eq(2)

From eq(1) & eq(2), we get the final answer**47.91 > 47.31 > 45.12 > 44.19**

(f) Arrange the numbers is descending orders**0.732 0.897, 0.321, 0.665**

**Step 01: Compare the integer value of decimals**

Integer for 0.732 ⟹ 0

Integer for 0.897 ⟹ 0

Integer for 0.321 ⟹ 0

Integer for 0.665 ⟹ 0

All the numbers are same, can’t conclude anything

**Step 02 : Compare the decimal values**

Decimal for 0.732 ⟹ .732

Decimal for 0.897 ⟹ .897

Decimal for 0.321 ⟹ .321

Decimal for 0.665 ⟹ .665

The whole number can be shown as 897 > 732 > 665 > 321

The similar will be the order for decimal numbers 0.897 > 0.732 > 0.665 > 0.321

Hence the above order is the required solution

(g) Arrange the decimals from highest to lowest**1.21, 2.6, 1.05, 2.55**

Make sure all the numbers have same decimal place value

1.21, 2.60, 1.05. 2.55

**Step 01: Compare the integer values**

Integer for 1.21 ⟹ 1

Integer for 2.60 ⟹ 2

Integer for 1.05 ⟹ 1

Integer for 2.55 ⟹ 2

we know that 2 > 1

Hence 2.60 & 2.55 are greater than 1.21 & 1.05 – – – -eq (1)

**Step 02 : Comparing decimal value of 2.60 & 2.55**

Decimal for 2.60 ⟹ .60

Decimal for 2.55 ⟹ .55

we know that .60 > .55

Hence 2.60 > 2.55 – – – -eq (2)

**Step 03: Comparing decimal value of 1.21 & 1.05**

Decimal for 1.21 ⟹ .21

Decimal for 1.05 ⟹ .05

we know that 0.21 > 0.05

Hence 1.21 > 1.05 – – – – eq (3)

From eq (1), (2) & (3) we conclude that :**2.60 > 2.55 > 1.21> 1.05**

(h) Arrange the decimals from high to low**2.51, 2.05, 3.0, 2.76**

Make sure all the numbers have same decimal place

2.51, 2.05, 3.00, 2.76

**Step 01**

Compare the integer values

Integer for 2.51 ⟹ 2

Integer for 2.05 ⟹ 2

Integer for 3.00 ⟹ 3

Integer for 2.76 ⟹ 2

We know that 3 > 2

Hence 3.00 > 2.51 & 2.05 & 2.76 – – – – eq(1)

**Step 02**

Compare decimal value of 2.51, 2.05 & 2.76

Decimal for 2.51 ⟹ 0.51

Decimal for 2.05 ⟹ 0.05

Decimal for 2.76 ⟹ 0.76

we know that 0.76 > 0.51 > 0.05

Hence 2.76 > 2.51 > 2.05 – – – -eq(2)

From equation (1) & (2) we get

3.00 > 2.76 > 2.51 > 2.05