# Reducing and Expanding Decimal Numbers

🏆Practice reduction and expansion of decimal fractions

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.

## Test yourself on reduction and expansion of decimal fractions!

Write the following decimal as a fraction and simplify:

$$0.75$$

## Example of reduction and expansion of decimal numbers

For example, if we closely observe the decimal number $8.70$ we will understand that:
The digit $8$ represents the units (in the whole part)
The digit $7$ represents the tenths
And the digit $0$ represents the hundredths.
Since there is no other digit representing the thousandths, we will understand that, in reality, there are no hundredths
The digit $0$ represents them.

Now, let's observe this decimal number $8.7$ and analyze it:
The digit $8$ represents the units (in the whole part)
The digit $7$ represents the tenths
And that's it.
We can clearly say that there are no hundredths or that the digit $0$ represents them, therefore
We can easily compare between $8.7$ and $8.70$
$8.7=8.70$
What we have done is, really, reduce the decimal number $8.70$ to $8.7$.

## Examples and exercises with solutions for reduction and amplification of decimal numbers

### 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:

$0.350$

### Video Solution

$\frac{7}{20}$

### Exercise #5

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

$0.8$

### Video Solution

$\frac{4}{5}$