Reducing and Expanding Decimal Numbers

🏆Practice reduction and expansion of decimal fractions

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 0.40.4 and 0.400.40 precisely because of the phrase we saw earlier.
In fact, 44 tenths is equivalent to 4040 hundredths.
Similarly, we can compare 2.562.56 and the decimal number2.5602.560 and also the decimal number 2.56002.5600

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 00, we are simplifying and expanding without realizing it.

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Test yourself on reduction and expansion of decimal fractions!

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

\( 0.36= \)

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Example of reduction and expansion of decimal numbers

For example, if we closely observe the decimal number 8.708.70 we will understand that:
The digit 88 represents the units (in the whole part)
The digit 77 represents the tenths
And the digit 00 represents the hundredths.
Since there is no other digit representing the thousandths, we will understand that, in reality, there are no hundredths
The digit 00 represents them.

Now, let's observe this decimal number 8.78.7 and analyze it:
The digit 88 represents the units (in the whole part)
The digit 77 represents the tenths
And that's it.
We can clearly say that there are no hundredths or that the digit 00 represents them, therefore
We can easily compare between 8.78.7 and 8.70 8.70
8.7=8.708.7=8.70
What we have done is, really, reduce the decimal number 8.708.70 to 8.78.7.


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= 0.36=

Video Solution

Step-by-Step Solution

Since there are two digits after the decimal point, we divide 36 by 100:

36100 \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:

36:4100:4=925 \frac{36:4}{100:4}=\frac{9}{25}

Answer

925 \frac{9}{25}

Exercise #2

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

0.5= 0.5=

Video Solution

Step-by-Step Solution

Since there is one digit after the decimal point, we divide 5 by 10:

510 \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:

5:510:5=12 \frac{5:5}{10:5}=\frac{1}{2}

Answer

12 \frac{1}{2}

Exercise #3

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

0.350 0.350

Video Solution

Step-by-Step Solution

Since there are three digits after the decimal point, we divide 350 by 1000:

3501000 \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:

350:501000:50=720 \frac{350:50}{1000:50}=\frac{7}{20}

Answer

720 \frac{7}{20}

Exercise #4

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

0.630 0.630

Video Solution

Step-by-Step Solution

Since there are three digits after the decimal point, we divide 630 by 1000:

6301000 \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:

630:101000:10=63100 \frac{630:10}{1000:10}=\frac{63}{100}

Answer

63100 \frac{63}{100}

Exercise #5

Write the following decimal fraction as an imaginary fraction and simplify:

6.9 6.9

Video Solution

Step-by-Step Solution

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+910 6+\frac{9}{10}

Since it can't be simplified further, the answer is:

6910 6\frac{9}{10}

Answer

6910 6\frac{9}{10}

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