Converting Decimals to Fractions

🏆Practice

To convert a decimal number to a simple fraction
we will ask ourselves how the decimal number
is read. If we use the word tenths, we will place 1010 in the denominator
If we use the word hundredths, we will place 100100 in the denominator
If we use the word thousandths, we will place 10001000 in the denominator.

The number itself will be placed in the numerator.
*If the integer figure differs from 00, we will note it next to the simple fraction.

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Write the following fraction as a decimal:

\( \frac{1}{10}= \)

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Converting Decimal Numbers to Fractions

Converting a simple fraction to a decimal number is easier than you might think.
To do it without making a mistake, we recommend reviewing the reading of decimal numbers and making sure you know how to do it well.
If you really know how to correctly read decimal numbers, you are guaranteed success when trying to convert a decimal number to a simple fraction.

As is known, decimal numbers are composed of an integer part and a fractional part which, in turn, is composed of tenths, hundredths, and thousandths.
When converting tenths, hundredths, and thousandths into the denominator of the fraction we obtain:

Magnificent! Now let's remember that, in order to correctly read a decimal number we must find out what its last digit symbolizes.

For example, how would we read the decimal number 0.870.87?
77 is its last digit and it represents the hundredths, therefore, we will call the decimal number 8787 hundredths.
Bingo! We have learned the signaling of the hundredths:

X100X \over 100

All that remains for us to do is to place 8787 in the numerator and get the simple fraction of the decimal number 0.870.87:


Let's practice a bit more:

Exercise 1

Convert the decimal number 0.30.3 to a fraction
Solution:
Let's ask ourselves, how is the decimal number read? 
33 tenths.
Therefore, we will use the notation for tenths and place 33 in the numerator: 3103 \over 10


Convert the decimal number 0.2000.200 to a fraction
Solution:
Let's ask ourselves, how is the decimal number read?
200200 thousandths.
Therefore, we will use the notation for thousandths and place 0.2000.200 in the numerator: 2001000200 \over 1000
Pay attention, if the fraction can be simplified, you can do so without changing its value:

210=2001000\frac{2}{10}=\frac{200}{1000}

And, indeed, we already know that: 0.200=0.2 0.200 = 0.2


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Exercise 2

Convert the decimal number 0.750.75 to a fraction
Solution:
Let's ask ourselves, how is the decimal number read? 
7575 hundredths.
Therefore, we will use the notation of hundredths and place 7575 in the numerator

7510075 \over100

We can reduce by dividing by 2525 and we will obtain: 343 \over 4


What happens when the figure of the whole part is not 00?
Simply place the whole number next to the fraction and continue operating according to what has been studied.
For example:
Convert the decimal number 4.254.25 to a fraction.
Solution:
Let's ask ourselves, how is the decimal number read?
44 and 2525 hundredths.
Therefore, we will use the notation of hundredths and place 2525 in the numerator. Let's not forget to add 44 wholes to its side:
4251004 \frac{25}{100}


Do you know what the answer is?
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