## Meaning of the Decimal Number

The decimal number represents, through the decimal point (or comma in certain countries), a simple fraction or a number that is not whole.
The decimal point divides the number in the following way:

You can read more in the assigned extended article

## Examples with solutions for Decimal Fractions - Advanced

### Exercise #1

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

### Step-by-Step Solution

Note that the decimal points are not written one below the other.

Therefore, the exercise is not written correctly.

Not true

### Exercise #2

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

La posición del punto decimal coincide.

### Step-by-Step Solution

Note that the decimal points are not written one below the other.

Therefore, the exercise is not written correctly.

Not true

### Exercise #3

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

### Step-by-Step Solution

Let's fill in the zeros in the empty space as follows:

$21.52\\+03.40\\$

Note that the decimal points are written one below the other

Therefore, the exercise is written in the correct form

True

### Exercise #4

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds..

### Step-by-Step Solution

Let's fill in the zeros in the empty space as follows:

$006.310\\+216.222\\\$We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.

True

### Exercise #5

Write the following decimal fraction as a simple fraction and simplify:

$0.36=$

### Step-by-Step Solution

Since there are two digits after the decimal point, we divide 36 by 100:

$\frac{36}{100}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 4, so:

$\frac{36:4}{100:4}=\frac{9}{25}$

$\frac{9}{25}$

### Exercise #6

Write the following decimal fraction as a simple fraction and simplify:

$0.350$

### Step-by-Step Solution

Since there are three digits after the decimal point, we divide 350 by 1000:

$\frac{350}{1000}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 50, so:

$\frac{350:50}{1000:50}=\frac{7}{20}$

$\frac{7}{20}$

### Exercise #7

Write the following decimal fraction as a simple fraction and simplify:

$0.630$

### Step-by-Step Solution

Since there are three digits after the decimal point, we divide 630 by 1000:

$\frac{630}{1000}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 10, so:

$\frac{630:10}{1000:10}=\frac{63}{100}$

$\frac{63}{100}$

### Exercise #8

Write the following decimal fraction as a simple fraction and simplify:

$0.5=$

### Step-by-Step Solution

Since there is one digit after the decimal point, we divide 5 by 10:

$\frac{5}{10}$

Now let's find the highest number that divides both the numerator and the denominator.

In this case, the number is 5, so:

$\frac{5:5}{10:5}=\frac{1}{2}$

$\frac{1}{2}$

### Exercise #9

Solve the following exercise and circle the appropriate answer:

### Step-by-Step Solution

Let's solve the exercise in order:

We'll subtract the tenths after the decimal point:

$1-0=1$

Finally, we'll subtract the whole numbers before the decimal point accordingly:

$2-2=0$

$2-1=1$

And we get:

$22.1\\-12.0\\10.1$

10.1

### Exercise #10

Solve the following exercise and circle the appropriate answer:

### Step-by-Step Solution

Let's solve the exercise in order:

We'll subtract the hundredths after the decimal point:

$9-3=6$

We'll subtract the tenths after the decimal point:

$2-1=1$

Finally, we'll subtract the whole numbers before the decimal point accordingly:

$3-2=1$

$1-1=0$

And we'll get:

$13.29\\-12.13\\01.16$

1.16

### Exercise #11

Solve the following exercise and circle the appropriate answer:

### Step-by-Step Solution

Let's solve the exercise in order:

We'll add up the hundredths after the decimal point:

$8+1=9$

We'll add up the tenths after the decimal point:

$3+4=7$

Finally, we'll add up the whole numbers before the decimal point accordingly:

$1+3=4$

$2+1=3$

And we get:

$21.38\\+13.41\\34.79$

34.79

### Exercise #12

Solve the following exercise and circle the appropriate answer:

### Step-by-Step Solution

Let's solve the exercise in order:

We'll add up the thousandths after the decimal point:

$2+3=5$

We'll add up the hundredths after the decimal point:

$1+1=2$

We'll add up the tenths after the decimal point:

$5+3=8$

Finally, we'll subtract the whole numbers before the decimal point:

$3+4=7$

And we get:

$3.512\\+4.313\\7.825$

7.825

### Exercise #13

Write the following decimal fraction as an imaginary fraction and simplify:

$11.3$

### Step-by-Step Solution

Let's write the decimal fraction as a mixed fraction.

Since there is one digit after the decimal point, we will divide 3 by 10 and add 11, as follows:

$11+\frac{3}{10}$

Since it cannot be simplified further, the answer is:

$11\frac{3}{10}$

$11\frac{3}{10}$

### Exercise #14

Write the following decimal fraction as an imaginary fraction and simplify:

$6.9$

### Step-by-Step Solution

Let's write the decimal fraction as a mixed fraction.

Since there is one digit after the decimal point, we'll divide 9 by 10 and add 6, as follows:

$6+\frac{9}{10}$

Since it can't be simplified further, the answer is:

$6\frac{9}{10}$

$6\frac{9}{10}$

### Exercise #15

Fill in the missing sign:

$19.88\text{ }_{—\text{ }}17.10$

### Step-by-Step Solution

Let's compare the numbers in the following way:

We notice that before the decimal point, both numbers start with 1

Then we have the number 9 versus the number 7

Since 9 is greater than 7, the appropriate sign is:

19.88 > 17.10