Reducing and Expanding Decimal Numbers

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.

Detailed explanation

Start practice

Test yourself on reduction and expansion of decimal fractions!

Write the following decimal as a fraction and simplify:

$$ 0.75 $$

Practice more now

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 fraction as a simple fraction and simplify:

$0.36=$

Video Solution

Step-by-Step Solution

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:

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

Answer

$\frac{9}{25}$

Exercise #2

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

$0.5=$

Video Solution

Step-by-Step Solution

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:

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

Answer

$\frac{1}{2}$

Exercise #3

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

$0.350$

Video Solution

Step-by-Step Solution

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:

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

Answer

$\frac{7}{20}$

Exercise #4

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

$0.630$

Video Solution

Step-by-Step Solution

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:

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

Answer

$\frac{63}{100}$

Exercise #5

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

$0.8$

Video Solution

Step-by-Step Solution

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:

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

Answer

$\frac{4}{5}$

Join Over 30,000 Students Excelling in Math!

Endless Practice, Expert Guidance - Elevate Your Math Skills Today

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:

$$ 0.8 $$

Start practice