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

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

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

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.

Are they the same numbers?

\( 0.05\stackrel{?}{=}0.5 \)

Comparing decimal numbers is an extremely simple matter if we know how to approach it.

We are here to teach you a simple and comfortable system that you can use from now on in all exercises involving the comparison of decimal numbers and succeed.

To determine if a certain decimal number is less than, greater than, or equal to another decimal number, we must observe them very carefully.

**We will call the system - Digit by Digit Analysis**

The first step is to analyze the numbers located before the decimal point, that is, to their left (the whole numbers).

If one of the decimal numbers has a whole number that is greater than the other, we can determine that this decimal number is larger than the second and there will be no need to continue analyzing the other digits.

Test your knowledge

Question 1

Are they the same numbers?

\( 0.1\stackrel{?}{=}0.10 \)

Question 2

Are they the same numbers?

\( 0.22\stackrel{?}{=}0.2 \)

Question 3

Are they the same numbers?

\( 0.23\stackrel{?}{=}0.32 \)

Mark $>,<$ or $=$

$60.23$______$45.78$

**Solution**:

Since $60$ is greater than $45$, there is no doubt that $60.23$ is greater than $45.78$

$60.23>45.78$

**Analysis concluded**

But what happens when the whole numbers are the same in both decimal numbers?

Let's move on to the second step:

If the two whole numbers are the same, we will move to the first digit after the decimal point. We will ask ourselves, which of them has the larger digit and, according to the answer, we will be able to determine which is the larger number.

If the first digit after the decimal point is also the same in both numbers, we will move to the next one, located to its right, and ask ourselves: in which of them is this digit larger?

In this way, we will proceed in order of location and analyzing each of the equal digits.

We will stop when we find a different digit.

Mark $>,<$ or $=$

$3.134$____$0.135$

Do not let the numbers deceive you, act according to the steps we have learned.

**Solution:**

Let's start by analyzing the whole numbers: $3$ is greater than $0$ and, therefore, the answer will be $>$

Do you know what the answer is?

Question 1

Are they the same numbers?

\( 0.25\stackrel{?}{=}0.250 \)

Question 2

Are they the same numbers?

\( 0.5\stackrel{?}{=}0.50 \)

Question 3

Are they the same numbers?

\( 0.6\stackrel{?}{=}0.60 \)

Mark $>,<$ or $=$

$4.154$_____$4.11$**Solution:**

Let's start analyzing:

The digit of the whole numbers is the same

The digit of the tenths is the same

The digit of the hundredths is different $5$ is greater than $1$ and, therefore, the answer will be $>$

Mark $>,<$ or $=$

$0.2$_____$0.130$

**Solution:**

Let's start analyzing:

The digit of the whole numbers is the same

The digit of the tenths is different $2$ is greater than $1$ and, therefore, the answer will be $>$.

Be careful, do not fall into the trap of thinking that, because $130$ is greater than $2$ the answer would be the opposite.

Operate according to the steps learned and you will not make a mistake.

Check your understanding

Question 1

Are they the same numbers?

\( 0.8\stackrel{?}{=}0.88 \)

Question 2

Which decimal number is greater?

Question 3

Are they the same numbers?

\( 0.02\stackrel{?}{=}0.002 \)

Mark $>,<$ or $=$

$9.98$_____$9.9$**Solution:**

Let's start analyzing

The digit of the whole numbers is the same

The digit of the tenths is the same

The digit of the hundredths is different, in one decimal there is $8$ and in the other there is no digit in the place of the hundredths, that is, $0$.

$8$ is greater than $0$ and the answer will be $<$.

Mark $>,<$ or $=$

$0.003$____$0.03$**Solution:**

Let's start analyzing

The digit of the whole numbers is the same

The digit of the tenths is the same

The digit of the hundredths is different $3$ is greater than $0$ and, therefore, the answer will be $<$

Do you think you will be able to solve it?

Question 1

\( 0.45\stackrel{?}{=}0.445 \)

Are they the same numbers?

Question 2

Choose the appropriate sign:

\( \frac{12}{10}?1.2 \)

Question 3

Choose the appropriate sign:

\( \frac{1}{3}?0.3 \)

Mark $>,<$ or $=$

$0.50$_____$0.5$

**Solution:**

Let's start analyzing

The digit of the whole numbers is equal

The digit of the tenths is equal

The digit of the hundredths is also equal, in one of the decimal numbers the hundredth digit, the $0$, is clearly visible and in the other it is not present, which means it is also $0$ therefore, these numbers are equal since there are no more digits to analyze. therefore, the answer will be $=$

Discover the number that lies between $1.7$ and $1.8$

**Solution:**

Sometimes we will come across questions like this. It should be clear to us that there are infinite numbers between the two that have been given to us, any digit we place (except for $0$) in the hundredths place will give a correct answer.

Possible correct solutions in this case:

$1.71, 1.78, 1.702, 1.75$

Test your knowledge

Question 1

Choose the appropriate sign:

\( \frac{2}{3}?0.6 \)

Question 2

Choose the appropriate sign:

\( \frac{3}{4}?0.8 \)

Question 3

Are they the same numbers?

\( 0.05\stackrel{?}{=}0.5 \)