Reducing and Expanding Decimal Numbers

Reduction and Expansion of Decimal Fractions - Examples, Exercises and Solutions

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:

$0.99000$

Step-by-Step Solution

To reduce the decimal fraction $0.99000$ , trailing zeros are removed. Therefore, $0.99000$ simplifies to $0.99$ . Hence, the reduced fraction is $0.99$ .

Answer

$0.99$

Exercise #2

Reduce the following fraction:

$0.600$

Step-by-Step Solution

To reduce the fraction $0.600$ , we look to express it in its simplest form. By removing trailing zeros, we arrive at $0.6$ , which is the same value and represents the simplest form of the number. The trailing zeros in a decimal do not affect its value.

Answer

$0.6$

Exercise #3

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 $0.84$ .

Answer

$0.84$

Exercise #4

Reduce the following fraction:

$0.25$

Step-by-Step Solution

To reduce the fraction $0.25$ , we note that it is already in its simplest form as a decimal fraction and cannot be reduced further. Therefore, the reduced form is $0.25$ itself.

Answer

$0.25$

Exercise #5

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

$0.75$

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Question 1

Reduce the following fraction:

$\( 0.40 \)$

Question 2

Reduce the following fraction:

$\( 0.56000 \)$

Question 3

Reduce the following fraction:

$\( 0.50 \)$

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Reduction and Expansion of Decimal Fractions

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