Decimals and fractions are both ways to represent parts of a whole, but they look quite different. Fractions are often used in everyday situations, from cooking recipes to dividing tasks. Understanding how to convert decimals to fractions is a fundamental math skill. Let’s break down the process step-by-step to make it easy!
Simple Steps to Turn Decimals into Fractions
Converting a decimal to a fraction is a straightforward process that involves a few key steps. Follow these instructions to easily transform any decimal into its fractional form:
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Step 1: Write the Decimal as a Fraction over One. Begin by writing your decimal number as the numerator of a fraction and ‘1’ as the denominator. This represents the decimal as a fraction in its most basic form.
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Step 2: Multiply to Remove the Decimal Point. Count the number of digits after the decimal point. For each digit, multiply both the numerator and the denominator by 10. If there is one digit after the decimal, multiply by 10. If there are two, multiply by 100 (10 x 10), and so on. This step effectively removes the decimal point from the numerator, turning it into a whole number.
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Step 3: Simplify the Fraction. Once you have a fraction with whole numbers in the numerator and denominator, simplify it to its lowest terms. This means finding the greatest common divisor (GCD) of both numbers and dividing both the numerator and the denominator by it. Simplifying makes the fraction easier to understand and use.
Example 1: Converting 0.75 to a Fraction
Let’s see these steps in action by converting the decimal 0.75 into a fraction.
Step 1: Write 0.75 over 1:
0.75 1
Step 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:
| × 100 |
|---|
| 0.75 1 |
| × 100 |
Notice how multiplying by 100 shifts the decimal point two places to the right, turning 0.75 into the whole number 75.
Step 3: Simplify the fraction. Now we need to simplify 75/100. We can see that both 75 and 100 are divisible by 25 (or simplify in stages by dividing by 5 twice, as shown in the original article).
| ÷ 25 | ||
|---|---|---|
| 75 100 | = | 3 4 |
| ÷ 25 |
Therefore, 0.75 is equal to the fraction 3 4.
Did you know? 75/100 is known as a decimal fraction, while 3 4 is called a common fraction.
Example 2: Converting 0.625 to a Fraction
Let’s try another example, converting the decimal 0.625 to a fraction.
Step 1: Write 0.625 over 1:
0.625 1
Step 2: Multiply by 1,000. There are three digits after the decimal point in 0.625, so we multiply both the numerator and the denominator by 1,000 (10 × 10 × 10 = 1,000):
625 1000
Step 3: Simplify the fraction. Simplify 625/1000. Both numbers are divisible by 25, and further simplification is possible.
| ÷ 125 | ||
|---|---|---|
| 625 1000 | = | 5 8 |
| ÷ 125 |
Thus, 0.625 is equivalent to the fraction 5 8.
Handling Whole Numbers with Decimals
When dealing with decimals that include a whole number part, like 2.35, we adjust our approach slightly. We focus on converting the decimal part into a fraction and then combine it with the whole number.
Example 3: Converting 2.35 to a Fraction
Let’s convert 2.35 into a fraction.
Isolate the decimal part: Set aside the whole number ‘2’ and focus on converting 0.35 to a fraction.
Step 1: Write 0.35 over 1:
0.35 1
Step 2: Multiply by 100: As there are two digits after the decimal point, multiply by 100.
35 100
Step 3: Simplify the fraction: Simplify 35/100 by dividing both by their greatest common divisor, which is 5.
| ÷ 5 |
|---|
| 35 100 |
| ÷ 5 |
Combine with the whole number: Now, bring back the whole number ‘2’. We combine it with the fraction 7 20 to form a mixed fraction.
Answer = 2 7 20
What About Repeating Decimals?
Repeating decimals, like 0.333…, require a slightly different approach. These decimals go on forever in a repeating pattern.
Example 4: Converting 0.333… to a Fraction
Let’s convert the repeating decimal 0.333… to a fraction.
Step 1: Let x equal the decimal:
Let x = 0.333…
Step 2: Multiply by 10:
10x = 3.333…
Step 3: Subtract the original equation:
Subtracting the first equation (x = 0.333…) from the second equation (10x = 3.333…) eliminates the repeating decimal part:
10x – x = 3.333… – 0.333…
9x = 3
Step 4: Solve for x:
Divide both sides by 9 to solve for x:
x = 3 9
Step 5: Simplify the fraction:
Simplify 3 9 by dividing both numerator and denominator by 3.
x = 1 3
So, 0.333… is equal to the fraction 1 3.
Example 5: Converting 0.444… to a Fraction
Let’s apply the same method to convert 0.444… to a fraction.
Step 1: Let x equal the decimal:
Let x = 0.444…
Step 2: Multiply by 10:
10x = 4.444…
Step 3: Subtract the original equation:
10x – x = 4.444… – 0.444…
9x = 4
Step 4: Solve for x:
x = 4 9
Therefore, 0.444… is equal to the fraction 4 9.
Explore Further
Converting decimals to fractions is a useful skill in many areas of mathematics and daily life. By following these simple steps and practicing with different examples, you can master this conversion.
To further your understanding and practice, you might find a Decimal to Fraction Calculator helpful for checking your answers and exploring more conversions.
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
