The Core Concept: Fractions ARE Division
The most important thing to understand about converting fractions to decimals is that a fraction IS a division problem. The fraction 3/4 literally means 3 divided by 4. The fraction line is a division symbol. So converting a fraction to a decimal is as simple as performing the division.
This single insight makes the entire topic straightforward. You do not need to memorize special rules or formulas. You just need to divide the numerator (top number) by the denominator (bottom number). The result is the decimal equivalent.
Why do fractions and decimals both exist if they represent the same number? Because each form is more convenient in different situations. Fractions are easier for exact arithmetic (1/3 is exact, while 0.333... is an approximation). Decimals are easier for comparison (is 5/8 or 7/11 larger? It is hard to tell from the fractions, but 0.625 vs 0.636 makes it obvious) and for real-world measurements (you would say 0.75 inches, not 3/4 inches, on a digital caliper).
Method 1: Long Division
The universal method for converting any fraction to a decimal is long division. Divide the numerator by the denominator.
Example: Convert 3/8 to a decimal. Divide 3 by 8. 8 does not go into 3, so add a decimal point and a zero: 3.0 divided by 8. 8 goes into 30 three times (24), remainder 6. Bring down another zero: 60. 8 goes into 60 seven times (56), remainder 4. Bring down another zero: 40. 8 goes into 40 exactly five times (40), remainder 0. Answer: 3/8 = 0.375.
Example: Convert 5/6 to a decimal. 6 into 5.000... 6 goes into 50 eight times (48), remainder 2. 6 goes into 20 three times (18), remainder 2. 6 goes into 20 three times (18), remainder 2. The remainder repeats, so the decimal repeats: 5/6 = 0.8333... = 0.83̅ (the bar over the 3 indicates it repeats forever).
If you are not comfortable with long division, use a calculator. Type 3 ÷ 8 and you get 0.375. The calculator is just performing the same long division electronically. Understanding the manual process is still valuable because it helps you recognize repeating patterns and predict when a decimal will terminate versus repeat.
Method 2: Equivalent Fractions with Denominators of 10, 100, or 1000
If you can rewrite the fraction with a denominator of 10, 100, or 1000, converting to a decimal is trivial. A denominator of 10 means one decimal place, 100 means two decimal places, and 1000 means three decimal places.
Example: Convert 3/5 to a decimal. Multiply top and bottom by 2: 3/5 = 6/10 = 0.6. Easy.
Example: Convert 7/20 to a decimal. Multiply top and bottom by 5: 7/20 = 35/100 = 0.35.
Example: Convert 3/25 to a decimal. Multiply top and bottom by 4: 3/25 = 12/100 = 0.12.
This method only works when the denominator is a factor of a power of 10. The numbers that work are 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000, and so on. If the denominator's only prime factors are 2 and 5, you can use this method. If it has any other prime factors (like 3, 7, or 11), the decimal will either repeat or you need long division.
Common Fractions to Decimals Chart
Memorizing these common conversions saves time on exams and in daily life. Here are the most frequently used fractions and their decimal equivalents:
Halves: 1/2 = 0.5.
Thirds: 1/3 = 0.333... (repeating), 2/3 = 0.666... (repeating).
Fourths: 1/4 = 0.25, 2/4 = 0.5, 3/4 = 0.75.
Fifths: 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8.
Sixths: 1/6 = 0.1666... (repeating), 5/6 = 0.8333... (repeating).
Eighths: 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875.
Tenths: 1/10 = 0.1, 3/10 = 0.3, 7/10 = 0.7, 9/10 = 0.9.
Knowing these by heart means you can quickly convert fractions you encounter in everyday math — tipping 20% (1/5), dividing something into quarters, measuring in eighths of an inch — without reaching for a calculator.
Terminating vs. Repeating Decimals
A terminating decimal has a finite number of digits after the decimal point. Examples: 0.5, 0.375, 0.12. A repeating decimal has a pattern of digits that repeats forever. Examples: 0.333..., 0.142857142857..., 0.1666...
How do you know which type a fraction will produce before you divide? Look at the denominator (in lowest terms). If the denominator's only prime factors are 2 and/or 5, the decimal terminates. If the denominator has any other prime factor (3, 7, 11, 13, etc.), the decimal repeats.
Examples: 1/8 terminates because 8 = 2³ (only 2s). 1/20 terminates because 20 = 2² × 5 (only 2s and 5s). 1/6 repeats because 6 = 2 × 3 (has a 3). 1/7 repeats because 7 is prime and is neither 2 nor 5. 1/12 repeats because 12 = 2² × 3 (has a 3).
Repeating decimals are often written with a bar (vinculum) over the repeating part: 1/3 = 0.̅3, 1/7 = 0.142857̅ (the entire sequence 142857 repeats). On handwritten work or when the bar notation is unavailable, an ellipsis (...) or the notation 0.3̅ is used.
Converting Mixed Numbers to Decimals
A mixed number like 3 1/4 has a whole number part (3) and a fractional part (1/4). To convert to a decimal, convert only the fractional part and add it to the whole number: 1/4 = 0.25, so 3 1/4 = 3.25.
Example: Convert 5 3/8 to a decimal. 3/8 = 0.375. So 5 3/8 = 5.375.
Example: Convert 2 1/3 to a decimal. 1/3 = 0.333... So 2 1/3 = 2.333...
Alternatively, convert the mixed number to an improper fraction first, then divide. 3 1/4 = 13/4. 13 ÷ 4 = 3.25. Both approaches give the same answer.
Converting Decimals Back to Fractions
For terminating decimals: write the decimal digits as the numerator and the appropriate power of 10 as the denominator, then simplify. 0.75 = 75/100 = 3/4. 0.125 = 125/1000 = 1/8. 0.6 = 6/10 = 3/5.
For repeating decimals: use algebra. To convert 0.333... to a fraction: Let x = 0.333... Multiply both sides by 10: 10x = 3.333... Subtract the original equation: 10x - x = 3.333... - 0.333... which gives 9x = 3, so x = 3/9 = 1/3.
For a repeating decimal like 0.272727...: Let x = 0.272727... Multiply by 100 (because two digits repeat): 100x = 27.272727... Subtract: 99x = 27, so x = 27/99 = 3/11.
This algebraic method works for any repeating decimal. The key is to multiply by the power of 10 that shifts the decimal point by exactly one full repeating cycle, so the repeating parts cancel when you subtract.
Comparing Fractions Using Decimals
One of the most practical uses of fraction-to-decimal conversion is comparing fractions. Which is larger: 5/8 or 7/11? Finding a common denominator (88) works but is tedious. Converting to decimals is faster: 5/8 = 0.625, 7/11 = 0.636... Since 0.636 > 0.625, we know 7/11 > 5/8.
This technique is invaluable on standardized tests where time matters. When a problem asks you to order fractions from least to greatest, convert them all to decimals and the order becomes obvious.
Example: Order these from least to greatest: 2/3, 5/8, 7/12, 3/4. Convert: 2/3 ≈ 0.667, 5/8 = 0.625, 7/12 ≈ 0.583, 3/4 = 0.75. Order: 7/12 < 5/8 < 2/3 < 3/4.
Practice Problems
Convert these fractions to decimals: (1) 7/8. [Answer: 0.875]. (2) 2/9. [Answer: 0.222... repeating]. (3) 11/20. [Answer: 0.55]. (4) 4/11. [Answer: 0.3636... repeating]. (5) 5 2/5. [Answer: 5.4].
Convert these decimals to fractions: (6) 0.35. [Answer: 7/20]. (7) 0.125. [Answer: 1/8]. (8) 0.444... [Answer: 4/9].
Comparison: Which is larger, 5/7 or 9/13? [Answer: 5/7 ≈ 0.714, 9/13 ≈ 0.692, so 5/7 is larger.]
If any of these problems give you trouble, snap a photo and send it to ScanSolve for a complete step-by-step solution showing the division process.