Decimals and fractions are two different ways to represent the same numerical value, but they are used in various contexts and calculations. Understanding how to convert between decimals and fractions is a fundamental skill in mathematics. Fractions are particularly useful in scenarios like cooking, crafting, or when you need to divide quantities into equal parts. This guide will walk you through the process of converting decimals to fractions in a clear, step-by-step manner.
Simple Steps to Convert Any Decimal to a Fraction
Converting a decimal to a fraction is easier than you might think. Just follow these straightforward steps:
Step 1: Write the Decimal Over One
Start by writing your decimal number as the numerator of a fraction and ‘1’ as the denominator. This essentially represents the decimal as a fraction out of one, which is the starting point for our conversion.
decimal / 1Step 2: Multiply to Remove the Decimal Point
Next, you need to eliminate the decimal point to get a whole number in the numerator. To do this, count the number of digits after the decimal point. For each digit, multiply both the numerator (the decimal) and the denominator (1) by 10.
- If there’s one digit after the decimal (e.g., 0.1), multiply by 10.
- If there are two digits (e.g., 0.25), multiply by 100 (10 × 10).
- For three digits (e.g., 0.125), multiply by 1000 (10 × 10 × 10), and so on.
This multiplication effectively shifts the decimal point to the right, turning the decimal into a whole number, while adjusting the denominator accordingly.
Step 3: Simplify the Fraction
Once you’ve removed the decimal point, you’ll have a fraction with a whole number numerator and a power of ten as the denominator. The final step is to simplify this fraction to its lowest terms. This means finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it. Simplifying makes the fraction easier to understand and use.
Let’s see these steps in action with some examples.
Example 1: Converting 0.75 to a Fraction
Step 1: Write 0.75 over 1
0.75 / 1Step 2: Multiply by 100
Since there are two digits after the decimal point in 0.75, we multiply both the numerator and the denominator by 100:
(0.75 × 100) / (1 × 100) = 75 / 100Step 3: Simplify the Fraction
Now, we simplify 75/100. Both 75 and 100 are divisible by 25 (or you can simplify in steps by dividing by 5 multiple times).
75 ÷ 25 = 3
100 ÷ 25 = 4So, 75/100 simplifies to 3/4.
Answer: 0.75 as a fraction is 3/4.
Note: 75/100 is known as a decimal fraction, while 3/4 is a common fraction.
Example 2: Converting 0.625 to a Fraction
Step 1: Write 0.625 over 1
0.625 / 1Step 2: Multiply by 1000
There are three digits after the decimal in 0.625, so we multiply by 1000:
(0.625 × 1000) / (1 × 1000) = 625 / 1000Step 3: Simplify the Fraction
Simplify 625/1000. Both numbers are divisible by 25 (and even 125 directly).
625 ÷ 125 = 5
1000 ÷ 125 = 8Thus, 625/1000 simplifies to 5/8.
Answer: 0.625 as a fraction is 5/8.
Dealing with Whole Numbers in Decimals
When you have a decimal with a whole number part, such as 2.35, you handle the decimal part separately and then combine it with the whole number to form a mixed fraction.
Example 3: Converting 2.35 to a Fraction
Separate the whole number and decimal: Keep the ‘2’ aside and focus on converting ‘0.35’.
Step 1: Write 0.35 over 1
0.35 / 1Step 2: Multiply by 100
Two digits after the decimal, so multiply by 100:
(0.35 × 100) / (1 × 100) = 35 / 100Step 3: Simplify the Fraction
Simplify 35/100. Both are divisible by 5.
35 ÷ 5 = 7
100 ÷ 5 = 20So, 35/100 simplifies to 7/20.
Combine with the whole number: Now, bring back the whole number ‘2’. The mixed fraction is formed by combining the whole number and the simplified fraction.
Answer: 2.35 as a fraction is 2 7/20.
Example 4: Converting 0.333 to a Fraction
Step 1: Write 0.333 over 1
0.333 / 1Step 2: Multiply by 1000
Three digits after the decimal, so multiply by 1000:
(0.333 × 1000) / (1 × 1000) = 333 / 1000Step 3: Simplify the Fraction
In this case, 333/1000 cannot be simplified further as 333 and 1000 share no common factors other than 1.
Answer: 0.333 as a fraction is 333/1000.
Special Case: Recurring Decimals
Recurring decimals, like 0.333…, which repeat infinitely, require a slightly different approach for conversion.
Example 5: Converting 0.333… to a Fraction
For recurring decimals, we use algebra to solve. Let x = 0.333…
Then 10x = 3.333…
Subtract x from 10x:
10x – x = 3.333… – 0.333…
9x = 3
x = 3/9
Simplify 3/9 to 1/3.
Answer: 0.333… as a fraction is 1/3.
Similarly, you can convert other recurring decimals by identifying the repeating pattern and using a similar algebraic method. Common recurring decimals and their fractional equivalents include:
- 0.1666… = 1/6
- 0.142857142857… = 1/7
- 0.111… = 1/9
- 0.0909… = 1/11
Example 6: Converting 0.444… to a Fraction
Let x = 0.444…
10x = 4.444…
10x – x = 4.444… – 0.444…
9x = 4
x = 4/9
Answer: 0.444… as a fraction is 4/9.
Use a Conversion Tool
For quick conversions, you can also use online tools like a Decimal to Fraction Calculator. These calculators can instantly convert decimals to fractions and simplify them for you.
Converting decimals to fractions is a useful skill that bridges the understanding between these two forms of numerical representation. By following these simple steps, you can easily convert any decimal into its fractional form and simplify it for practical use. Whether for schoolwork, cooking, or everyday problem-solving, mastering this conversion will prove to be beneficial.
Introduction to Fractions
Introduction to Decimals
Decimal to Fraction Converter
Converting Fractions to Decimals
Converting Decimals to Percents
Multiplying Fractions
Dividing Fractions
Simplifying Fractions
Equivalent Fractions
Fractions Index
Decimals Index
