# Reduction and expansion of decimal fractions - Examples, Exercises and Solutions

The topic of reducing and expanding decimal numbers is extremely easy.
All you need to remember is the following phrase:

#### If we add the digit 0 at the end of a decimal number (to the right), the value of the decimal number will not change.

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.

## Practice Reduction and expansion of decimal fractions

### Exercise #1

Write the following decimal as a fraction and simplify:

$0.75$

### Video Solution

$\frac{3}{4}$

### Exercise #2

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

$0.36=$

### Video Solution

$\frac{9}{25}$

### Exercise #3

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

$0.58$

### Video Solution

$\frac{29}{50}$

### Exercise #4

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

$0.8$

### Video Solution

$\frac{4}{5}$

### Exercise #5

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

$0.5=$

### Video Solution

$\frac{1}{2}$

### Exercise #1

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

$0.350$

### Video Solution

$\frac{7}{20}$

### Exercise #2

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

$0.630$

### Video Solution

$\frac{63}{100}$

### Exercise #3

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

$1.4$

### Video Solution

$1\frac{2}{5}$

### Exercise #4

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

$2.6$

### Video Solution

$2\frac{3}{5}$

### Exercise #5

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

$6.9$

### Video Solution

$6\frac{9}{10}$

### Exercise #1

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

$11.3$

### Video Solution

$11\frac{3}{10}$

### Exercise #2

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

$16.4$

### Video Solution

$16\frac{2}{5}$

### Exercise #3

Fill in the missing sign:

$0.305\text{ }_{—\text{ }}0.30$

>

### Exercise #4

Fill in the missing sign:

$0.8\text{ }_{—\text{ }}0.08$

>

### Exercise #5

Fill in the missing sign:

$0.008\text{ }_{—\text{ }}0.08$