Convert Decimal to Fraction

Converting a decimal to a fraction is the process of changing a number in decimal form into a fraction, which represents the same value in terms of parts of a whole number. Converting decimals into fractions is a key skill that helps clarify values and is useful in various practical situations.

Decimal: A decimal represents a number with a whole part and a fractional part, separated by a decimal point. Example: 0.619, 50.5, etc.
Fraction: A fraction represents a part of a whole, expressed with a numerator (top) showing parts taken and a denominator (bottom) showing total parts. Example: 619/1000, etc.

Steps for Decimal to Fraction Conversion

Here are the steps to convert a decimal number into a fraction:

Step 1: First, divide the decimal number by 1.

Example: Decimal number 0.565

On applying step 1:

0.565/1

Step 2: For every decimal point in the numerator multiply 10 for both numerator and denominator.

In this example, 2 numbers are given after the decimal point, so multiply with 10 two times for both numerator and denominator.

(0.565 × 10 × 10 x 10)/(1 × 10 × 10 x 10)
= 565/1000

Step 3: Perform simplification on the fraction formed from Step 2 until further simplification is not possible.

565/1000
= 113/200

These are the 3 steps that one must follow while converting from decimal to fraction.

Handling Repeating Decimals

Repeating decimals, like 0.333… (where 3 repeats infinitely), are a bit trickier to convert into fractions.

Here's how you can handle them:

1. Let x = 0.333….
2. Multiply both sides by 10 to shift the decimal point:
   10x = 3.333…
3. Subtract the original equation from this new equation:
   10x - x = 3.333… - 0.333…
   This simplifies to:
   9x = 3
4. Solve for x by dividing both sides by 9:
   x = 3/9, which simplifies to 1/3.

Thus, 0.333… = 1/3. For more complex repeating decimals, the process is similar, but the multiplication factor changes depending on the number of repeating digits.

Converting Negative Decimals to Fractions

The process of converting negative decimals to fractions is almost identical to the steps we've discussed. The only difference is the negative sign. For example, to convert -0.625:

1. Write it as -0.625/1.
2. Multiply both top and bottom by 1000 (since there are three digits after the decimal).
3. Simplify the fraction -625/1000 by dividing both by 125, giving -5/8.

Negative decimal to fraction conversion requires keeping the negative sign intact throughout the process.

Read more:

• Convert Fractions to Decimals
• Convert Binary Fractions to Decimal

Solved Examples on Decimals to Fraction Conversion

Question 1: Convert a decimal 0.1 to a fraction

Solution:

Step - 1 Divide decimal with 1
= 0.1/1

Step - 2 As there is only 1 number after point so multiply 10 one time to both numerator and denominator.
= 0.1 × 10/1 × 10 = 1/10

Step - 3 The above generated can't be simplified further so we consider the above fraction 1/10 as final result.

So fraction of 0.1 = 1/10

Question 2: Convert a decimal 6.25 to a fraction

Solution:

Step - 1 Divide decimal with 1
= 6.25/1

Step - 2 As there are 2 numbers after point so multiply 10 two times with both numerator and denominator.
= 6.25 × 10 × 10/1 × 10 × 10 = 625/100

Step - 3 This 625/100 fraction can be simplified to,
625/100 = 125/20 = 25/4

So fraction of 6.25 = 25/4

Question 3: Convert a decimal 6.25 into a mixed fraction.

Solution:

When a whole number is present before point in decimal number then separate that whole number from decimal number and follow the 3 steps for conversion.
6.25 = 6 + 0.25

Step - 1 Consider the digits that are after the decimal point i.e., 0.25 and Divide decimal with 1
= 0.25/1

Step - 2 As there are 2 numbers after point so multiply 10 two times with both numerator and denominator.
= 0.25 × 10 × 10/1 × 10 × 10 = 25/100

Step - 3 This 25/100 fraction can be simplified to
25/100 = 5/20 = 1/4

Add the separated digit 6 (done before step-1) to formed fraction.
So fraction of 6.25 = 6\frac{1}{4}

Question 4: Convert a decimal 4.372 into a mixed fraction.

Solution:

For conversion into mixed fraction, separate the whole number part before the decimal point from decimal value and follow the above specified 3 steps on numbers after decimal points.

4.372 = 4 + 0.372

Step - 1 Consider the digits that are after the decimal point i.e., 0.372 and Divide decimal with 1
= 0.372/1

Step - 2 As there are 3 numbers after point so multiply 10 three times with both numerator and denominator.
= 0.372 × 10 × 10 × 10/1 × 10 × 10 × 10 = 372/1000

Step - 3 This 372/1000 fraction can be simplified to,
372/1000 = 93/250

Add the separated digit 4 (done before step-1) to formed fraction
So fraction of 4.372 =  4\frac{93}{250}

Question 5: Convert a decimal 0.33 to a fraction

Solution:

Step - 1 Divide decimal with 1
= 0.33/1

Step - 2 As there are 2 numbers after point so multiply 10 two times with both numerator and denominator.
= 0.33 × 10 × 10/1 × 10 × 10 = 33/100

Step - 3 This 33/100 fraction can't be simplified so it can be leaved as it is

So fraction of 0.33 = 33/100 

Question 6: Convert a decimal 0.3333... to a fraction

Solution:

Step - 1 Divide decimal with 1
= 0.3333..../1

Note: For this kind of recurrence number i.e., 3 is recurring for infinite times we can't multiply 10 for each decimal point. In this case we multiply numerator and denominator with 3.

Step - 2 As this is a recurrence number we multiply 3 with numerator and denominator.
0.3333.... × 3/1 × 3 = 0.9999..../3

Step - 3 Simply the above fraction.
As 0.9999... is close to 1, round up the numerator to 1.
0.9999..../3 can be simplified to 1/3.

So fraction of 0.3333... = 1/3 

Question 7: Convert a negative decimal -0.75 to a fraction

Solution:

Step 1: Divide the negative decimal by 1.
−0.75/1

Step 2: Multiply both the numerator and the denominator by 100 to eliminate the decimal points (since there are two decimal places).−0.75×100/1×100=−75/100

Step 3: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 25.
−75/100=−3/4

The fraction form of -0.75 is −3/4.

Question 8: Convert a repeating decimal 0.666... to a fraction

Solution:

Step 1: Let x=0.666...

Step 2: To eliminate the repeating decimal, multiply x by 10 (since the repeating part has one digit).
10x=6.666

Step 3: Subtract the original x from this new equation to isolate the repeating part.
10x − x = 6.666 − 0.666
9x = 6

Step 4: Solve for x by dividing both sides by 9.
x = 6/9
= 2/3.