Converting Decimals to Fractions

🏆Practice converting decimal fractions to simple fractions and mixed numbers

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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Test yourself on converting decimal fractions to simple fractions and mixed numbers!

einstein

Write the following fraction as a decimal:

\( \frac{5}{100}= \)

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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:

B1 - Composition of decimal numbers

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}


Examples and exercises with solutions for converting decimal numbers to fractions

Exercise #1

Write the following fraction as a decimal:

510= \frac{5}{10}=

Video Solution

Step-by-Step Solution

Write the simple fraction in decimal form

5.0 5.0

Since the fraction is divided by 10, move the decimal point one place to the left and get:

.5 .5

Complete the zero to the left of the decimal point and get:

0.5 0.5

Answer

0.5

Exercise #2

Write the following fraction as a decimal:

710= \frac{7}{10}=

Video Solution

Step-by-Step Solution

Write the simple fraction in decimal form

7.0 7.0

Since the fraction is divisible by 10, move the decimal point one place to the left and get:

.7 .7

Let's add the zero to the left of the decimal point and get:

0.7 0.7

Answer

0.7

Exercise #3

0.171= 0.171=

Video Solution

Step-by-Step Solution

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the decimal point represents tenths

Two numbers after the decimal point represent hundredths

Three numbers after the decimal point represent thousandths

And so on

In this case there are three numbers after the decimal point so the number is divided by 1000

Write the fraction in the following way:

01711000 \frac{0171}{1000}

We will remove the extra zeros and get:

1711000 \frac{171}{1000}

Answer

1711000 \frac{171}{1000}

Exercise #4

Write the following fraction as a decimal:

5100= \frac{5}{100}=

Video Solution

Answer

0.05

Exercise #5

Write the following fraction as a decimal:

3100= \frac{3}{100}=

Video Solution

Answer

0.03

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