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You’re doing homework, checking a recipe, or staring at a calculator screen, and there it is: 0.33333. It looks so familiar that your brain whispers, “That’s one-third, right?” Well… almost. The truth is a little more interesting, and it’s exactly why so many people search for 0.33333 as a fraction.
In this guide, we’ll answer the question once and for all, show you the math step by step, and clear up the confusion between the decimal that ends and the decimal that never does.
Quick Answer: What is 0.33333 as a Fraction?
If you just want the answer, here it is. 0.33333 as a fraction depends on whether the 3s stop or go on forever:
- 0.33333 (exactly five 3s, then it stops) = 33333/100000
- 0.33333… (the 3s repeat forever) = 1/3
Most of the time, when someone types 0.33333 into a search bar, they mean the repeating version, which is one-third. But if your problem treats 0.33333 as an exact, terminating number, the answer is 33333/100000. Let’s see why.
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What is 0.33333 as a Fraction? The Step-by-Step Method
Converting a terminating decimal into a fraction follows a simple process. Let’s break down 0.33333 step by step.
Step 1: Write the decimal over 1
Step 2: Count the decimal places
There are five digits after the decimal point, so multiply the numerator and denominator by 105, or 100,000.
Step 3: Simplify if possible
To simplify, look for a common factor of 33,333 and 100,000. Since 100,000 is divisible only by factors of 2 and 5, and 33,333 is not divisible by either 2 or 5, there is no common factor to cancel.
0.33333 as a Fraction in Simplest Form
Therefore, 0.33333 = 33333/100000
Quick Fact
The fraction 33333/100000 cannot be reduced further because 33,333 and 100,000 have a greatest common factor of 1.
0.33333 Repeating as a Fraction
Now for the fun part. What if those 3s go on forever? Mathematicians write this as 0.3̅ (or 0.333...). To find the fraction behind it, we can use a little algebraic trick.
Let x = 0.33333...
Multiply both sides by 10 to shift the decimal point one place:
Now subtract the original equation from the new one. The endless tails of 3s cancel perfectly:
9x = 3
And there it is: 0.33333 repeating equals 1/3. Divide 1 by 3 on any calculator and you'll see the 3s march on forever, since 3 never divides evenly into 1.
So Why Are There Two Answers?
Think of it like this: 0.33333 is a very close neighbor of 1/3, but not quite the same house. The difference is tiny:
≈ 1/300,000
That's about three millionths, which is small enough to ignore in everyday life, but large enough to matter in a math exam. Teachers often want to see whether you noticed the difference between a terminating decimal and a repeating one.
Terminating Decimal
The digits stop. 0.33333
Answer: 33333/100000
Repeating Decimal
The digits never stop. 0.333...
Answer: 1/3
-0.33333 as a Fraction
What about a negative sign? Good news: negatives don't change the method at all. Just carry the minus sign along. -0.33333 as a fraction is:
- -0.33333 (terminating) = -33333/100000
- -0.33333... (repeating) = -1/3
Quick Reference Table
Bookmark this little cheat sheet for the next time a decimal like this pops up.
| Decimal | As a Fraction | Simplest Form |
|---|---|---|
| 0.33333 | 33333/100000 | 33333/100000 |
| 0.33333... (repeating) | 3/9 | 1/3 |
| -0.33333 | -33333/100000 | -33333/100000 |
| -0.33333... (repeating) | -3/9 | -1/3 |
Real-Life Examples of 0.33333 (or 1/3)
You meet one-third more often than you think:
- Cooking: A ⅓ cup of flour is roughly 0.333 cups.
- Sharing: Splitting a pizza among three friends gives each person 0.3333... of it.
- Money and discounts: A “one-third off” sale takes about 33.33% off the price.
- Time: 20 minutes is one-third of an hour, or 0.3333... hours.
Recommended reading: What Is Partial Products in Math? Definition & Examples
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Conclusion
So, what is 0.33333 as a fraction? The short answer is 33333/100000 when the decimal ends, and 1/3 when those 3s keep dancing forever. Once you know the place-value trick for terminating decimals and the “multiply and subtract” trick for repeating ones, you can convert almost any decimal into a fraction with confidence.
Next time you spot 0.33333 on your screen, you’ll know exactly what’s hiding behind those tiny 3s. Happy calculating!
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Frequently Asked Questions
Not exactly. 1/3 is 0.333... with the 3s going on forever. 0.33333 is a rounded, five-digit version that is extremely close but slightly smaller.
33333/100000, since 33,333 and 100,000 share no common factors other than 1.
If it terminates: -33333/100000
If it repeats: -1/3
