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

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Test yourself on reduction and expansion of decimal fractions!

Reduce the following fraction:

$$ 0.30 $$

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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

Reduce the following fraction:

$0.7000$

Step-by-Step Solution

If you have a fraction like $0.7000$ , you can simplify it by removing all the trailing zeros. Thus, it reduces down to $0.7$ . All the trailing zeros to the right of the decimal point in a number can be eliminated without changing the value of the number.

Answer

$0.7$

Exercise #2

Reduce the following fraction:

$0.5$

Step-by-Step Solution

To reduce $0.5$ , recognize that it's already in its simplest form as a decimal fraction.

When expressed as a fraction of 1, $0.5$ is equivalent to $\frac{1}{2}$ , which means $0.5$ is simplified.

Answer

$0.5$

Exercise #3

Reduce the following fraction:

$0.75$

Step-by-Step Solution

To reduce $0.75$ , notice that it represents $\frac{75}{100}$ .

The greatest common divisor of 75 and 100 is 25, so divide both the numerator and the denominator by 25.

This reduces the fraction to $\frac{3}{4}$ , which is $0.75$ when expressed as a decimal.

Answer

$0.75$

Exercise #4

Reduce the following fraction:

$0.56000$

Step-by-Step Solution

To reduce the decimal fraction $0.56000$ , we eliminate trailing zeros that have no significance after the decimal point. Thus, $0.56000$ becomes $0.56$ .
Therefore, the reduced fraction is $0.56$ .

Answer

$0.56$

Exercise #5

Reduce the following fraction:

$0.8400$

Step-by-Step Solution

To reduce the decimal fraction $0.8400$ , we eliminate the trailing zeros. Thus, $0.8400$ becomes $0.84$ . As a result, the reduced fraction is $0.84$ .