Decimal to Fraction Converter: Free Tool, Steps & Charts

Stand in any hardware store and you can watch the same small drama play out at the drill-bit rack. Someone's phone says they need a 0.3125-inch hole; the bits on the wall are labeled 5/16. Two ways of writing the exact same number — and a purchase that stalls until somebody bridges them. That bridge is what this page is about: how to convert decimals to fractions (and back) quickly, exactly, and with enough understanding that you never have to memorize a chart again.

At the top you'll find our free decimal to fraction converter — a tool we built specifically for this guide — followed by the complete method behind it: step-by-step instructions for terminating decimals, the algebra trick for repeating decimals, mixed numbers, percentages, negative values, printable-style conversion charts, and answers to the questions people actually type into Google at 11 p.m. before a math test.

▶  Jump to the free converter

Decimal Converter Embed Code for Your Website:

Numbers tell stories. They help us understand the world, measure our progress, and make sense of complex information. But sometimes, the way we write numbers can feel like speaking different languages. A decimal speaks one way, a fraction tells another story, and binary whispers in the language of computers. That's why this tool exists - to bridge those gaps and make numbers accessible to everyone.

You can copy this code and embed it on your website, giving your visitors a powerful yet simple tool that transforms how they interact with numbers. Whether they're students grappling with math homework, developers debugging code, or professionals analyzing data, this Decimal Converter makes the translation between number formats feel effortless and even enjoyable.

The Decimal Converter is an intuitive, interactive tool that allows your website visitors to instantly convert between decimals, fractions, percentages, and binary numbers. Simply enter a value in any format, and watch as all other formats update simultaneously - turning what could be a frustrating calculation into a moment of clarity and understanding.

This tool is essential for educational websites, coding blogs, financial platforms, scientific resources, or any site where numbers play a starring role. It's more than just a converter - it's a bridge between worlds, helping people see the connections between different ways of representing value.

The code is available in six global languages to welcome visitors from every corner of the planet: English - Spanish - French - Arabic - Chinese - Hindi.

You can easily switch the converter language by changing the parameter in the URL: ?lang=en

Available languages: en - es - fr - ar - zh - hi

1- Isolated iFrame Code (Ideal for Articles and Pages):

If you're writing a tutorial about mathematics, programming, or data analysis, this method allows you to embed the tool directly within your content. The isolated iframe ensures a clean, distraction-free experience, so your readers can experiment with number conversions right alongside your explanations - turning abstract concepts into tangible understanding.

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2- Flexible Script (Suitable for Sidebars and Templates):

This method is perfect for sidebars, footers, or widget areas where you want the tool to be always within reach. The converter loads smoothly and elegantly, becoming a trusted resource that helps your visitors navigate the fascinating world of numbers - whether they're checking their work, learning something new, or simply satisfying their curiosity about how different number systems relate to one another.

Just add these lines to your website's code, and the Decimal Converter will appear instantly, ready to help. It's fully responsive by design, ensuring a beautiful experience on desktops, tablets, and smartphones.

 <div class="tooliqo-tool" data-tool="decimal-converter" data-lang="en"></div>
<script src="https://tools.tooliqo.co/embed.js" async></script>

Note: The Decimal Converter works in real-time, providing instant conversions as your visitors type or adjust values. No page reloads required - just a smooth, intuitive experience that turns number confusion into number confidence. Because when we understand numbers better, we understand our world a little more clearly.

Decimals and fractions: two names, one number

Here's the mental shift that makes everything else easy: a decimal and a fraction aren't two different kinds of number. They're two different notations for the same point on the number line. 0.75 and 34 are the same value wearing different clothes — the way "half past seven" and "7:30" are the same time.

A fraction answers the question "how many parts of what size?" The bottom number (the denominator) tells you how many equal pieces the whole was cut into; the top number (the numerator) tells you how many of those pieces you have. Three quarters: cut into 4, take 3.

A decimal answers the same question, but it insists the pieces come in sizes of ten: tenths, hundredths, thousandths, and so on. Each digit after the decimal point is a count of one of those sizes. In 0.375, the 3 means three tenths, the 7 means seven hundredths, the 5 means five thousandths. Add them up — 300/1000 + 70/1000 + 5/1000 — and you get 375/1000, which simplifies to 3/8. Decimals are just fractions with a strong opinion about denominators.

That "strong opinion" is also why decimals sometimes struggle. Ten's prime factors are 2 and 5, so any fraction whose denominator is built only from 2s and 5s converts to a clean, terminating decimal. But a denominator with any other prime factor — a 3, a 7, an 11 — can never be expressed exactly in tenths and hundredths. The decimal digits start repeating forever instead: 1/3 = 0.333..., written compactly as 0.(3). Every terminating or repeating decimal is a rational number, which means it has an exact fraction form — and finding it is a mechanical process you can learn in the next two sections.

A one-minute history of the decimal point

Fractions are ancient — Egyptian scribes were composing them from unit fractions four thousand years ago — but the decimal fraction is surprisingly young. The earliest systematic treatment we know of comes from al-Uqlidisi, a scholar working in Damascus around 952 CE, whose arithmetic manual shows halving numbers past the units place and marking where the whole part ends. Five centuries later, Jamshid al-Kashi in Samarkand pushed the idea to astonishing precision, computing the circle constant to sixteen decimal places for astronomical tables — decimal fractions as a serious scientific instrument, not a curiosity.

Europe caught on late. The Flemish engineer Simon Stevin's 1585 pamphlet De Thiende ("The Tenth") made the case that decimal fractions would simplify commerce, surveying, and coinage — he even predicted decimal currency — though his notation (little circled indices after each digit) was clunky. The clean separator we use today spread in the early 1600s, and then promptly split in two: the English-speaking world settled on the point (3.14) while much of Europe, Latin America, and beyond settled on the comma (3,14). Both are correct; they're regional dialects of the same idea.

Decimal to fraction, step by step

For any decimal that ends — a terminating decimal — the conversion is two moves. This is the exact procedure the converter above performs (and narrates) when you type something like 0.32 or 4.05.

1. Count the decimal places and write the digits over 1 followed by that many zeros. Two places means hundredths; three means thousandths. 0.32 → 32/100.
2. Reduce to lowest terms. Find the greatest common divisor (GCD) of the top and bottom, and divide both by it. GCD(32, 100) = 4, so 32/100 = 8/25.

That's genuinely all there is. Let's run it on a few numbers people search for constantly:

What is 0.625 as a fraction?

Three decimal places, so 0.625 = 625/1000. The GCD of 625 and 1000 is 125. Divide both: 625/1000 = 5/8. If you don't spot a big GCD immediately, reduce in stages — halve, halve again, divide by 5 — you'll land in the same place.

What is 0.375 as a fraction?

0.375 = 375/1000. GCD(375, 1000) = 125, giving 3/8. Notice the pattern with the previous example: eighths produce decimals ending in .125, .375, .625, .875. Once you've seen it, you'll never forget it — it's half of reading a tape measure.

What is 4.05 as a fraction?

Whole numbers ride along for free. 4.05 = 405/100, GCD 5, so 81/20 — or, keeping the whole part separate, the mixed number 4 1/20. Both are correct; which you want depends on what you're doing next (more on that below).

Why the trick works

Multiplying a decimal by 10 slides the point one place right. So multiplying 0.32 by 100 gives the whole number 32 — which means 0.32 must equal 32 divided by 100. You're not doing anything mysterious; you're just undoing the place-value system. The only judgment call is the reduction step, and even that is pure mechanics: the Euclidean algorithm (repeatedly replace the larger number with the remainder of dividing it by the smaller) finds the GCD of any two numbers, no factoring insight required. It's the same algorithm running inside the converter — on integers of unlimited size, which matters more than you'd think once repeating decimals enter the picture.

Repeating decimals to fractions: the algebra method

Repeating decimals scare people, and honestly the fear is misplaced — the method is a genuinely satisfying piece of algebra, three lines long, and once it clicks you can convert any repeating decimal without a chart. It's also the exact routine our converter prints in its "Show steps" panel, so you can check your homework line against line.

The idea: call the mystery number x, then multiply it by powers of ten until two copies of it have identical infinite tails. Subtract those two copies, and the infinite tails annihilate each other, leaving an ordinary equation with whole numbers.

Example 1: pure repeating — what is 0.(45) as a fraction?

1. Let x = 0.454545...
2. The repeating block is 2 digits long, so multiply by 100: 100x = 45.454545...
3. Subtract the first line from the second. The tails cancel: 99x = 45, so x = 45/99. Reduce by the GCD (9): x = 5/11.

Example 2: the classic — what is 0.(3) as a fraction?

One repeating digit, so multiply by 10: 10x = 3.333... Subtract x = 0.333... to get 9x = 3, hence x = 1/3. Thirty seconds, no memorization.

Example 3: a non-repeating prefix — what is 1.2(7) as a fraction?

This is the case that trips people up: 1.2777... has one digit (the 2) before the repetition starts. The fix is to use two multiplications — one to slide the point past the non-repeating part, one to slide it a full repeating block further:

1. x = 1.2777...
2. Multiply by 10 (past the prefix): 10x = 12.777...
3. Multiply by 100 (one block further): 100x = 127.777...
4. Subtract line 2 from line 3: 90x = 115, so x = 115/90 = 23/18 — the mixed number 1 5/18.

All three examples are one pattern, and it compresses into a formula worth pinning above a desk:

Try it on 1.2(7): all digits form 127, the non-repeating digits form 12, and the difference is 115. One repeating digit means one 9; one non-repeating decimal digit means one 0 — denominator 90. You get 115/90 = 23/18 instantly, same answer as the long way. For 0.(81): 81 over 99 = 9/11. For 0.2(3): (23 − 2)/90 = 21/90 = 7/30.

Fraction to decimal: divide, and know what's coming

Going from a fraction to a decimal is a single operation — divide the numerator by the denominator — but there's real skill in predicting what the answer will look like before you divide.

The terminating test: look at the denominator

Fully reduce the fraction first. Then factor the denominator. If it contains only 2s and 5s, the decimal terminates — guaranteed. Any other prime in there and the decimal repeats forever.

• 7/8: denominator 8 = 2×2×2 → terminates: 0.875
• 3/20: 20 = 2×2×5 → terminates: 0.15
• 5/12: 12 = 2×2×3 → that 3 forces repetition: 0.41(6)
• 5/7: 7 is prime and not 2 or 5 → repeats with a long block: 0.(714285)

Why the digits must eventually cycle

Long division by b can only ever produce remainders between 0 and b−1. Either you hit remainder 0 (the decimal stops) or, within at most b−1 steps, a remainder you've already seen comes around again — and from that moment the digits replay in a loop. That's why 1/7 has a repeating block of exactly 6 digits (142857, the famous cyclic number), and why no fraction with denominator 7 can repeat with a longer period. The converter on this page detects the cycle the honest way: it performs the long division with exact integer arithmetic, watches for the first repeated remainder, and marks the block — then reports the repeating block length right under the result.

Worked example: 7/8 to a decimal

7 ÷ 8: 8 into 70 goes 8 times (64), remainder 6; into 60 goes 7 times (56), remainder 4; into 40 goes exactly 5. Remainder 0 — done: 0.875. As predicted by the denominator test, it terminated.

Mixed numbers and improper fractions

A mixed number (like 2 3/4) and an improper fraction (like 11/4) are, once again, the same value in different outfits. Mixed numbers read naturally — nobody asks for "eleven quarters of a cup of flour" — while improper fractions are far easier to calculate with. Converting between them:

Mixed to improper: 2 3/5 = (2×5 + 3)/5 = 13/5. Improper to mixed: for 11/4, 4 goes into 11 twice with remainder 3, so 2 3/4. And to decimal, either route works: 11 ÷ 4 = 2.75, or convert just the fraction part (3/4 = 0.75) and add the whole 2.

One convention to keep straight: 2 3/5 means 2 plus 3/5, never 2 times 3/5. The space is doing the work of a plus sign. (The converter parses it that way too — type 2 3/5 with the space and it reads it as a mixed number.)

Percentages: the third form of the same number

A percentage is just a fraction that has committed to the denominator 100 — per centum, "per hundred." Which means every decimal, fraction, and percent is inter-convertible with two tiny rules:

The traps are all about direction. Moving to percent, the number gets bigger (the point slides two places right); moving from percent, it gets smaller. 0.375 = 37.5%, not 3.75%. And repeating decimals stay repeating as percentages: 1/3 = 0.(3) = 33.(3)% — the honest way to write what people usually round to 33.33%.

Negative decimals and fractions

Nothing new is needed: set the sign aside, convert the positive value, then put the sign back on the result. So −0.625 converts through 625/1000 to −5/8, and −2.25 becomes −9/4, or the mixed number −2 1/4 — where, by convention, the minus applies to the whole thing (negative two-and-a-quarter), not just the 2. The converter follows the same convention and accepts a leading minus on any input format.

Conversion charts and quick values

Understanding the method beats memorizing tables — but some equivalents come up so often that having them at your fingertips saves real time. Every value below was computed with exact arithmetic (the same engine as the converter), so you can treat these charts as reference-grade.

Everyday decimal–fraction–percent chart

Two families are worth committing to memory outright. The eighths (.125, .375, .625, .875) unlock every imperial tape measure and drill index. The ninths are a party trick: n/9 = 0.(n), so 2/9 is 0.(2), 7/9 is 0.(7), on and on — and the same logic gives n/99 = 0.(0n) for two-digit blocks, which is precisely why 45/99 collapsed to 0.(45) back in the algebra section.

Quick values from the converter

These are the preset chips built into the tool above — the numbers we chose because, between them, they exercise every conversion path this article covers. Tap any chip in the converter and you'll see the matching row come to life, complete with steps:

Inside the converter: what makes this one different

There are plenty of decimal-fraction calculators online, so it's fair to ask why we built another. The short answer: most of them round. Ours doesn't — and around that one decision, a set of features grew that we haven't seen combined anywhere else. Here's the honest tour.

Exact arithmetic, not floating point

Open your browser's console right now and type 0.1 + 0.2. You'll get 0.30000000000000004. That's not a bug in your browser; it's the nature of the binary floating-point numbers almost all software calculates with — they can't represent most decimal values exactly, so tiny errors creep into everything. A converter built on floats will quietly tell you that some messy fraction "equals" your decimal when it's actually only close.

This tool sidesteps the entire problem: every conversion runs on arbitrary-precision integer arithmetic (BigInt), representing your number as an exact ratio of two whole numbers from the first keystroke. When it says 0.(45) = 5/11, that's an identity, not an approximation. When results are shown rounded — the little ≈ 0.4545454545... line under a repeating result — the tool marks them with the approximation symbol so exact and approximate are never confused.

One smart input, five formats

There's no dropdown asking what kind of number you're about to type. The parser recognizes the format on its own: a plain decimal (0.375), a fraction (7/8), a mixed number with a space (2 3/5), a repeating decimal in parentheses notation (1.2(7)), or a percentage (15%) — each optionally negative. Whatever you give it, you get all four forms back at once: decimal, reduced fraction, mixed number (when it applies), and percent, each with its own copy button.

It converts while you type

Results update live, a beat after you stop typing — no button-hunting. And it's polite about it: half-finished input like 0. or 3/ doesn't trigger an error flash mid-thought. Press Enter (or the Convert button) to commit a value, Escape to clear, or the little dice for a random worked example when you're exploring.

It shows its work — real algebra, not a summary

Every conversion comes with a numbered "Show steps" panel that mirrors this article. For terminating decimals you'll see the power-of-ten setup and the exact GCD used to reduce. For repeating decimals you get the genuine algebra — x = 0.(45), 100x = 45.(45), subtract, solve — the same three lines a teacher would write on the board. If you're a student, it's a worked solution for any number you can invent; if you're a parent helping with homework, it's a memory refresher on demand.

A picture of the fraction

Next to every fraction result sits a small ring, filled exactly as much as the fractional part. It sounds minor; it isn't. Seeing 5/11 rendered as "a bit under half a circle" is the fastest sanity check there is — if you expected roughly three-quarters and the ring disagrees, you've caught a mistake before it cost you anything.

Repeating decimals in and out

Most calculators print 0.4166666667 and call it a day. This one performs the long division exactly, detects the cycle, and writes 0.41(6) — the true value — along with the repeating block length. It accepts that notation as input too, so a result you copied yesterday can be pasted back in as today's starting point without losing a single digit of precision.

Small conveniences that add up

Recent history: your last six conversions wait as one-tap chips (stored only in your own browser). Copy all: one click grabs every form as tidy labeled lines, ready for notes or a message. Share: generates a link with your number baked in — open it and the converter loads pre-filled and already solved, which is quietly great for tutors sending practice problems. Six languages (English, Arabic with full right-to-left layout, French, Spanish, Chinese, Hindi) with automatic detection. Dark mode that follows your system. And it all runs entirely in your browser — nothing you type is sent to any server, which also means it keeps working on a flaky connection once the page has loaded.

Where you'll actually use this

In the kitchen

Recipes live in fractions; scaling lives in decimals. Halving a recipe that calls for 3/4 cup means computing 0.75 ÷ 2 = 0.375 — and then converting back, because your measuring cups say 3/8, not "0.375". Scale by 1.5 instead and 2/3 cup becomes 0.(6) × 1.5 = 1 exact cup — a case where the repeating decimal, handled exactly, lands on a perfectly clean answer that a rounded 0.67 would have missed.

In the workshop

Imperial measurement is fraction country: tape measures marked in 1/16ths, drill bits in 1/64ths, lumber in quarters. Meanwhile every digital caliper, CAD program, and 3D-printer slicer speaks decimal. The 0.3125-inch hole from the top of this page is the 5/16 bit; a caliper reading of 0.4375 is a 7/16 wrench. Woodworkers quietly do this conversion dozens of times per project — it's the single most common real-world use we hear about. A pocket rule worth keeping: one sixty-fourth of an inch is 0.015625, so multiplying any caliper reading by 64 and rounding tells you the nearest fractional drill size in one step.

With money and percentages

Interest rates, discounts, and tips are percent on the label but decimal in the math. A 15% discount is a multiplication by 0.15; "half off, then an extra third off the sale price" is 1/2 × 2/3 = 1/3 of the original — a two-second fraction calculation that decimal-only thinking turns into a rounding mess. Finance is also where exactness stops being pedantic: fractions of a cent, compounded, become real money.

In school (on both sides of the desk)

Decimal-fraction fluency is a load-bearing wall in the middle-school curriculum — it's where place value, division, ratios, and percent all meet. Students use a tool like this to check work, not skip it: do the conversion by hand, then compare against the steps panel line by line. Teachers use the share links to hand out problems that arrive pre-loaded, and the dice button to generate discussion examples on the spot.

In data, code, and music

Programmers meet this the hard way, via 0.1 + 0.2. Analysts meet it when a spreadsheet shows 0.6667 and a report needs "2/3 of respondents." Musicians live in it permanently: a dotted quarter note is 3/8 of a whole note, and time signatures are literally fractions. Once you see the pattern, it's everywhere — which is exactly why the conversion deserves to be automatic in your head and instant in your browser.

Practice: ten conversions, answers hidden until you're ready

Reading about a skill and having it are different things, so here's a graded set — easy terminating decimals up to a two-part repeater. Do them on paper (or in your head), then tap each answer to check. If one goes wrong, type it into the converter and read the steps panel: it will show you exactly which move differed from yours.

1. Convert 0.85 to a fraction.
   Answer

   17/20 — 85/100 reduced by 5. As a percent: 85%.
2. Convert 0.048 to a fraction.
   Answer

   6/125 — 48/1000, GCD 8. Trailing thousandths are where people miscount zeros; three decimal places means three zeros.
3. Convert 3.125 to an improper fraction and a mixed number.
   Answer

   25/8, i.e. 3 1/8. (3125/1000, GCD 125.)
4. Convert 0.(7) to a fraction.
   Answer

   7/9 — the ninths pattern, instantly.
5. Convert 0.5(4) to a fraction.
   Answer

   49/90 — (54 − 5) over one 9 and one 0.
6. Convert 2.1(36) to a fraction.
   Answer

   47/22 — (2136 − 21)/990 = 2115/990, reduced by 45. Mixed: 2 3/22. This is the hardest kind you'll meet; if you got it, you're done learning this topic.
7. Convert 9/16 to a decimal.
   Answer

   0.5625 — denominator is pure 2s, so it had to terminate.
8. Convert 7/11 to a decimal.
   Answer

   0.(63) — elevenths repeat in two-digit blocks: multiples of 9 (09, 18, 27, ... 63 for 7/11).
9. Convert 4 2/3 to a decimal and a percent.
   Answer

   4.(6) and 466.(6)% — via 14/3.
10. Convert −0.375 to a fraction.
    Answer

    −3/8 — convert the positive value, then restore the sign.

Spreadsheet corner: fractions in Excel and Google Sheets

Since so much decimal-to-fraction work ends up in a spreadsheet anyway, two formulas worth knowing:

In Excel or Google Sheets, =TEXT(A1,"?/?") renders the value in A1 as a single-digit fraction, and =TEXT(A1,"# ??/??") as a mixed number with up to two digits — so 0.375 displays as 3/8 and 2.75 as 2 3/4. You can get the same effect without formulas via Format → Number → Fraction.

The catch — and it's a real one — is that spreadsheets approximate to the nearest representable fraction within the digit budget you allowed. Ask for "?/?" on 0.454545... and you'll get 5/11 only if you're lucky with the digit setting; ask for sixteenths on a value that isn't one and it will cheerfully print the nearest sixteenth as if it were exact. Repeating decimals are also already damaged on entry, because the cell stored a rounded binary float before your format ever saw it. So: spreadsheets are fine for displaying friendly fractions of clean values, but for establishing what a number exactly is — especially anything repeating — do the conversion in exact arithmetic first (by hand with the methods above, or with the converter), then carry the true fraction into the sheet.

Common mistakes (and how to dodge them)

Dividing the wrong way. A fraction bar means "top divided by bottom." 3/4 is 3 ÷ 4 = 0.75, never 4 ÷ 3. If your "conversion" of a proper fraction comes out bigger than 1, you've flipped it.

Stopping before lowest terms. 32/100 is a correct fraction for 0.32 and also an unfinished one. Teachers dock points for it, and rightly so — 8/25 is the same value with all the shared factors wrung out. When in doubt, run the Euclidean algorithm; when in more doubt, the converter's steps show the exact GCD it divided by.

Rounding a repeating decimal too early. Writing 1/3 as 0.33 bakes in a 1% error before you've even started; multiply by 300 and you're off by a full unit. Keep values as fractions (or in 0.(3) notation) through the middle of a calculation and round only at the very end.

The percent double-slip. Converting 0.375 to "3.75%" (should be 37.5%) or 15% to "1.5" (should be 0.15) — both are the same error of moving the decimal point the wrong direction, or only one place. Anchor yourself with a value you know cold: one half is 50%.

Misreading mixed-number signs. −2 1/4 means −(2 + 1/4) = −2.25. It does not mean −2 + 0.25. Convert the positive value, then apply the sign to the whole result.

Trusting a floating-point answer to be exact. If a calculator tells you 0.416666666667 "equals" 5/12, it's approximating twice — once in the division, once in the display. For checking homework or cutting expensive material, use exact arithmetic and notation that can say repeating out loud.

Frequently asked questions

How do I convert a decimal to a fraction?

Write the digits after the point over a power of ten (one zero per decimal place), then reduce by the greatest common divisor. Example: 0.14 = 14/100 = 7/50. For decimals with a whole part, carry it along: 4.05 = 405/100 = 81/20.

How do I turn a repeating decimal into a fraction?

Set x equal to the decimal, multiply by powers of ten so two copies share the same infinite tail, subtract, and solve. Shortcut: (all digits − non-repeating digits), over one 9 per repeating digit followed by one 0 per non-repeating digit. So 0.2(3) = (23 − 2)/90 = 7/30.

What is 0.375 as a fraction?

3/8. Work: 375/1000, GCD 125. As a percent it's 37.5%.

What is 0.625 as a fraction?

5/8 — 625/1000 reduced by 125. Its neighbors on the tape measure: 0.125 = 1/8, 0.375 = 3/8, 0.875 = 7/8.

Is 0.999... really equal to 1?

Yes — exactly, not approximately. The algebra: 10x = 9.999..., subtract x to get 9x = 9, so x = 1. Two notations, one number.

How can I tell if a fraction gives a terminating or repeating decimal?

Reduce it, then factor the denominator. Only 2s and 5s → terminating. Any other prime factor → repeating, with a block at most (denominator − 1) digits long.

How do I convert a mixed number to an improper fraction?

Multiply the whole part by the denominator, add the numerator, keep the denominator: a b/c = (a×c + b)/c. So 2 3/5 = 13/5.

Do all decimals have an exact fraction form?

All terminating and repeating decimals do — that's the definition of a rational number. Decimals that never terminate and never repeat (like pi or the square root of 2) are irrational and have no exact fraction, only approximations.

Why does my calculator say 0.1 + 0.2 = 0.30000000000000004?

Because standard calculators and programming languages use binary floating-point, which can't represent most decimal values exactly — 0.1 in binary is itself a repeating "decimal." The converter on this page avoids the issue entirely by computing with exact integer ratios, so 0.1 + 0.2 territory simply never arises.

One number, four names

If this page did its job, the drill-bit standoff from the introduction now looks almost funny: 0.3125 and 5/16 were never two numbers to reconcile, just one number introduced twice. Decimal, fraction, mixed number, percent — four names, one value, and a pair of mechanical procedures (a power of ten and a GCD one way; a long division the other, with three lines of algebra for the repeaters) that translate between them on demand.

Keep the converter at the top of this page bookmarked for the moments when speed matters, use its steps panel for the moments when understanding matters, and share it with the student, cook, or woodworker in your life who's still squinting at a chart. If you find a number it handles in a way that surprises you — or one you think it should handle better — we genuinely want to hear about it.

Built and maintained by Tooliqo.co. The converter runs entirely in your browser, stores nothing on our servers, and is free to use — today and as far ahead as we can promise.