# Comparing Decimal Fractions - Examples, Exercises and Solutions

Comparing decimal numbers is done using the system: Digit-by-digit analysis

#### First step:

Analyze the whole numbers: the decimal number with the larger whole number will be the greater of the two.

#### Second step:

Analyze the digits that come after the decimal point (only in the case where the whole numbers are equal)
We will move from digit to digit (starting with the tenths, then the hundredths, and so on)
If they continue to be equal, we will proceed with the comparison of the following digits.
If they are different, we will be able to determine which number is larger.

## Examples with solutions for Comparing Decimal Fractions

### Exercise #1

Which decimal number is greater?

### Step-by-Step Solution

Let's convert the decimal numbers to simple fractions and compare them:

0.24 is divided by 100 because there are two digits after the decimal point, so:

$0.24=\frac{24}{100}$

0.25 is divided by 100 because there are two digits after the decimal point, so:

$0.25=\frac{25}{100}$

Let's compare the numbers in the numerator:

\frac{25}{100}>\frac{24}{100}

Therefore, the larger number is 0.25

$0.25$

### Exercise #2

Are they the same numbers?

$0.8\stackrel{?}{=}0.88$

### Step-by-Step Solution

We will add 0 to the number 0.8 in the following way:

$0.8=0.80$

And we will discover that the numbers are not identical

No

### Exercise #3

Are they the same numbers?

$0.05\stackrel{?}{=}0.5$

### Step-by-Step Solution

We will add 0 to the number 0.5 in the following way:

$0.5=0.50$

And we will discover that the numbers are not identical

No

### Exercise #4

Are they the same numbers?

$0.23\stackrel{?}{=}0.32$

### Step-by-Step Solution

Let's look at the numbers after the decimal point.

Since 23 and 32 are not the same number, the numbers are not identical.

No

### Exercise #5

Are they the same numbers?

$0.22\stackrel{?}{=}0.2$

### Step-by-Step Solution

We will add 0 to the number 0.2 in the following way:

$0.2=0.20$

And we will discover that the numbers are not identical

No

### Exercise #6

Are they the same numbers?

$0.1\stackrel{?}{=}0.10$

### Step-by-Step Solution

We will add 0 to the number 0.1 in the following way:

$0.1=0.10$

And we will discover that the numbers are indeed identical

Yes

### Exercise #7

Are they the same numbers?

$0.25\stackrel{?}{=}0.250$

### Step-by-Step Solution

We will add 0 to the number 0.25 in the following way:

$0.25=0.250$

And we will discover that the numbers are identical

Yes

### Exercise #8

Are they the same numbers?

$0.6\stackrel{?}{=}0.60$

### Step-by-Step Solution

We will add 0 to the number 0.6 in the following way:

$0.6=0.60$

And we will discover that the numbers are identical

Yes

### Exercise #9

Are they the same numbers?

$0.5\stackrel{?}{=}0.50$

### Step-by-Step Solution

We will add 0 to the number 0.5 in the following way:

$0.5=0.50$

And we will discover that the numbers are identical

Yes

### Exercise #10

Are they the same numbers?

$0.02\stackrel{?}{=}0.002$

### Step-by-Step Solution

We will add 0 to the number 0.02 in the following way:

$0.02=0.020$

And we will discover that the numbers are not identical

No

### Exercise #11

$0.45\stackrel{?}{=}0.445$

Are they the same numbers?

### Step-by-Step Solution

Just as the number 45 is not equal to 445, similarly 0.45 is not equal to 0.445,

even though their values are relatively very close.

This can be seen more clearly in the form of a regular fraction -

45/100 is not equal to 445/1000

No

### Exercise #12

Which decimal number is greater?

### Step-by-Step Solution

Let's convert the decimal numbers to simple fractions and compare them:

0.33 is divided by 100 because there are two digits after the decimal point, so:

$0.33=\frac{33}{100}$

0.34 is divided by 100 because there are two digits after the decimal point, so:

$0.34=\frac{34}{100}$

Let's compare the numbers in the numerator:

\frac{34}{100}>\frac{33}{100}

Therefore, the larger number is 0.34

0.34

### Exercise #13

Which decimal number is greater?

### Step-by-Step Solution

Let's convert the two numbers to fractions -

19/100

20/100

It's clear to us that 20 is greater than 19, and by the same logic, 0.2 is greater than 0.19, even though it might appear smaller to us because it has fewer digits.

$0.2$

### Exercise #14

Which decimal number is greater?

### Step-by-Step Solution

Let's convert the decimal numbers to simple fractions and compare them:

0.2 is divided by 10 because there is only one digit after the decimal point, so:

$0.2=\frac{2}{10}$

0.25 is divided by 100 because there are two digits after the decimal point, so:

$0.25=\frac{25}{100}$

Let's compare the numbers in the denominator:

\frac{25}{100}>\frac{2}{10}

Therefore, the larger number is 0.25

$0.25$

### Exercise #15

Which decimal number is greater?

### Step-by-Step Solution

Let's convert the decimal numbers to simple fractions and compare them:

0.25 is divided by 100 because there are two digits after the decimal point, so:

$0.25=\frac{25}{100}$

0.26 is divided by 100 because there are two digits after the decimal point, so:

$0.26=\frac{26}{100}$

Let's compare the numbers in the numerator:

\frac{26}{100}>\frac{25}{100}

Therefore, the larger number is 0.26

$0.26$