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

All you need to remember is the following phrase:

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.

Write the following decimal as a fraction and simplify:

\( 0.75 \)

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 $8.7$.

Write the following decimal as a fraction and simplify:

$0.75$

$\frac{3}{4}$

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

$0.36=$

$\frac{9}{25}$

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

$0.58$

$\frac{29}{50}$

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

$0.350$

$\frac{7}{20}$

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

$0.8$

$\frac{4}{5}$

Test your knowledge

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:

\( 0.58 \)

Question 3

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

\( 0.350 \)

Related Subjects

- Fractions
- A fraction as a divisor
- How do you simplify fractions?
- Simplification and Expansion of Simple Fractions
- Common denominator
- Hundredths and Thousandths
- Part of a quantity
- Placing Fractions on the Number Line
- Numerator
- Denominator
- Decimal Fractions
- What is a Decimal Number?
- Addition and Subtraction of Decimal Numbers
- Comparison of Decimal Numbers
- Converting Decimals to Fractions
- Multiplication and Division of Decimal Numbers by 10, 100, etc.
- Multiplication of Decimal Numbers
- Division of Decimal Numbers
- Repeating Decimal
- Decimal Measurements
- Density