# Ordering and Comparing Decimals

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

Using 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

Compare 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

Step 01: Compare the integers number

Integer 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

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

First 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

First 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

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

First 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

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

First 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