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 $8.7$ .