🏆Practice converting decimal fractions to simple fractions and mixed numbers

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Decimal Fractions - Basic

Converting Decimal Fractions to Simple Fractions and Mixed Numbers

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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 $10$ in the denominator If we use the word hundredths, we will place $100$ in the denominator If we use the word thousandths, we will place $1000$ in the denominator.

The number itself will be placed in the numerator. *If the integer figure differs from $0$, we will note it next to the simple fraction.

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 $0.87$? $7$ is its last digit and it represents the hundredths, therefore, we will call the decimal number $87$ hundredths. Bingo! We have learned the signaling of the hundredths:

$X \over 100$

All that remains for us to do is to place $87$ in the numerator and get the simple fraction of the decimal number $0.87$:

Let's practice a bit more:

Exercise 1

Convert the decimal number $0.3$ to a fraction Solution: Let's ask ourselves, how is the decimal number read? $3$ tenths. Therefore, we will use the notation for tenths and place $3$ in the numerator: $3 \over 10$

Convert the decimal number $0.200$ to a fraction Solution: Let's ask ourselves, how is the decimal number read? $200$ thousandths. Therefore, we will use the notation for thousandths and place $0.200$ in the numerator: $200 \over 1000$ Pay attention, if the fraction can be simplified, you can do so without changing its value:

$\frac{2}{10}=\frac{200}{1000}$

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

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Convert the decimal number $0.75$ to a fraction Solution: Let's ask ourselves, how is the decimal number read? $75$ hundredths. Therefore, we will use the notation of hundredths and place $75$ in the numerator

$75 \over100$

We can reduce by dividing by $25$ and we will obtain: $3 \over 4$

What happens when the figure of the whole part is not $0$? Simply place the whole number next to the fraction and continue operating according to what has been studied. For example: Convert the decimal number $4.25$ to a fraction. Solution: Let's ask ourselves, how is the decimal number read? $4$ and $25$ hundredths. Therefore, we will use the notation of hundredths and place $25$ in the numerator. Let's not forget to add $4$ wholes to its side: $4 \frac{25}{100}$

Examples and exercises with solutions for converting decimal numbers to fractions

Exercise #1

Write the following fraction as a decimal:

$\frac{1}{100}=$

Video Solution

Step-by-Step Solution

Let's write the simple fraction as a decimal fraction

$1.0$

Since the fraction divides by 100, we move the decimal point once to the left and get:

$.010$

We'll add the zero before the decimal point and get:

$0.010=0.01$

Answer

0.01

Exercise #2

Write the following fraction as a decimal:

$\frac{20}{100}=$

Video Solution

Step-by-Step Solution

Let's write the simple fraction as a decimal fraction

$20.0$

Since the fraction divides by 100, we move the decimal point once to the left and get:

$.200$

We'll add the zero before the decimal point and get:

$0.200=0.2$

Answer

0.2

Exercise #3

Write the following fraction as a decimal:

$\frac{3}{100}=$

Video Solution

Step-by-Step Solution

Let's write the simple fraction as a decimal fraction

$3.0$

Since the fraction divides by 100, we move the decimal point once to the left and get:

$.030$

We'll add the zero before the decimal point and get:

$0.030=0.03$

Answer

0.03

Exercise #4

Write the following fraction as a decimal:

$\frac{11}{100}=$

Video Solution

Step-by-Step Solution

Let's write the simple fraction as a decimal fraction

$11.0$

Since the fraction divides by 100, we move the decimal point once to the left and get:

$.110$

We'll add the zero before the decimal point and get:

$0.110=0.11$

Answer

0.11

Exercise #5

Write the following fraction as a decimal:

$\frac{5}{100}=$

Video Solution

Step-by-Step Solution

Let's write the simple fraction as a decimal fraction

$5.0$

Since the fraction divides by 100, we'll move the decimal point once to the left and get:

$.050$

We'll add the zero before the decimal point and get: