The topic of reducing and expanding decimal numbers is extremely easy.

All you need to remember is the following phrase:

Question Types:

The topic of reducing and expanding decimal numbers is extremely easy.

All you need to remember is the following phrase:

**What does this tell us?**

Let's look at some examples:

We can compare $0.4$ and $0.40$ precisely because of the phrase we saw earlier.

In fact, $4$ tenths is equivalent to $40$ hundredths.

Similarly, we can compare $2.56$ and the decimal number$2.560$ and also the decimal number $2.5600$

**What does this have to do with the simplification and amplification of decimal numbers?**

When we compare these decimal numbers and do not calculate the meaning of $0$, we are simplifying and expanding without realizing it.

Question 1

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

\( 0.36= \)

Question 2

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

\( 0.5= \)

Question 3

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

\( 0.350 \)

Question 4

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

\( 0.630 \)

Question 5

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

\( 6.9 \)

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

$0.36=$

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:

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

$\frac{9}{25}$

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

$0.5=$

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:

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

$\frac{1}{2}$

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

$0.350$

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:

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

$\frac{7}{20}$

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

$0.630$

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:

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

$\frac{63}{100}$

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

$6.9$

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:

$6\frac{9}{10}$

$6\frac{9}{10}$

Question 1

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

\( 11.3 \)

Question 2

Fill in the missing sign:

\( 0.8\text{ }_{—\text{ }}0.08 \)

Question 3

Fill in the missing sign:

\( 0.35\text{ }_{—\text{ }}0.135 \)

Question 4

Fill in the missing sign:

\( 19.88\text{ }_{—\text{ }}17.10 \)

Question 5

Fill in the missing sign:

\( 101.0\text{ }_{—\text{ }}102.1 \)

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

$11.3$

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:

$11\frac{3}{10}$

$11\frac{3}{10}$

Fill in the missing sign:

$0.8\text{ }_{—\text{ }}0.08$

To compare which is greater, we will compare the numbers by adding 0 to 0.8 as follows:

$0.80\text{?}0.08$

Let's note that before the decimal point, we have 0 in both numbers

After the decimal point, we have 8 versus 0

Since 8 is greater than 0, the appropriate sign is:

0.80 > 0.08

>

Fill in the missing sign:

$0.35\text{ }_{—\text{ }}0.135$

To compare which is greater, we'll compare the numbers by adding 0 to 0.35 as follows:

$0.350\text{?}0.135$

We notice that before the decimal point, we have 0 in both numbers

After the decimal point, we have 3 versus 1

Since 3 is greater than 1, the appropriate sign is:

0.350 > 0.135

>

Fill in the missing sign:

$19.88\text{ }_{—\text{ }}17.10$

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

>

Fill in the missing sign:

$101.0\text{ }_{—\text{ }}102.1$

Let's compare the numbers in the following way:

We notice that before the decimal point, both numbers start with 1 and then 0

After that, the numbers are different, 1 versus 2

Since 2 is greater than 1, the appropriate sign is:

101.0 < 102.1

<

Question 1

Fill in the missing sign:

\( 202.1\text{ }_{—\text{ }}202.01 \)

Question 2

Fill in the missing sign:

\( 66.101\text{ }_{—\text{ }}6.6101 \)

Question 3

Fill in the missing sign:

\( 2.021\text{ }_{—\text{ }}20.21 \)

Question 4

Fill in the missing sign:

\( 24.305\text{ }_{—\text{ }}24.315 \)

Question 5

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

\( 0.8 \)

Fill in the missing sign:

$202.1\text{ }_{—\text{ }}202.01$

Let's compare the numbers in the following way:

We notice that before the decimal point, both numbers start with 202

After the decimal point, we notice that the number is 1 versus 0

Since 1 is greater than 0, the appropriate sign is:

202.1 > 202.01

>

Fill in the missing sign:

$66.101\text{ }_{—\text{ }}6.6101$

Let's compare the numbers in the following way:

We notice that before the decimal point, we have the number 66 versus the number 6

Since 66 is greater than 6, the appropriate sign is:

66.101 > 6.6101

>

Fill in the missing sign:

$2.021\text{ }_{—\text{ }}20.21$

Let's compare the numbers in the following way:

We notice that before the decimal point, we have the numbers 2 and 20

Since 20 is greater than 2, the appropriate sign is:

2.021 < 20.21

<

Fill in the missing sign:

$24.305\text{ }_{—\text{ }}24.315$

Let's compare the numbers in the following way:

We notice that before the decimal point, both numbers start with 24

After the decimal point, we have the number 3

Then the numbers are 0 versus 1

Since 1 is greater than 0, the appropriate sign is:

24.305 < 24.315

<

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

$0.8$

Since there is one digit after the decimal point, we divide 8 by 10:

$\frac{8}{10}$

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

In this case, the number is 2, so:

$\frac{8:2}{10:2}=\frac{4}{5}$

$\frac{4}{5}$