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 fraction as a simple fraction and simplify:

\( 0.36= \)

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 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:

$6\frac{9}{10}$

$6\frac{9}{10}$

Test your knowledge

Question 1

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

\( 0.5= \)

Question 2

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

\( 0.350 \)

Question 3

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

\( 0.630 \)

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