Step-by-step methods for moving between fractions, decimals, and percentages in either direction, with a full reference table.
Published September 7, 2026 · Reviewed by the Ihsabha Editorial Team
Fractions, decimals, and percentages are three different ways of writing the exact same value. A recipe calling for 3/4 cup, a calculator showing 0.75, and a discount tag reading 75% are all describing an identical quantity — just dressed in different notation for different purposes. Knowing how to move fluidly between the three, in either direction, is one of the most broadly useful math skills there is, whether you're reading a nutrition label, splitting a bill, or working through a school assignment. This guide covers every conversion direction with clear steps and worked examples.
Each format has situations where it's simply more convenient than the others. Fractions are exact and intuitive for physical division — cutting a pizza into eighths, or splitting a chore three ways. Decimals are the easiest format for adding, subtracting, and typing into a calculator. Percentages are the clearest for comparison at a glance — it's far easier to compare 62% and 58% instantly than to compare 31/50 and 29/50. None of the three formats is objectively "better"; each is a tool suited to a different job, and converting between them is simply a matter of translation. For a deeper look, our guide on Reverse Percentage: How to Find the Original Number covers this in more detail. Rather than working this out by hand every time, the Fraction to Percent Calculator can handle the whole calculation for you.
To convert any fraction to a decimal, divide the numerator (top number) by the denominator (bottom number).
Some fractions, like 1/3 or 5/6, produce decimals that repeat forever. In everyday use these are simply rounded to a reasonable number of places (0.333 or 0.83), but it's worth knowing the repeating pattern exists rather than assuming the decimal terminates cleanly.
To convert a decimal to a fraction, write it over a power of 10 matching its number of decimal places, then simplify.
The same process works for any terminating decimal: 0.6 becomes 6/10, which simplifies to 3/5; 0.125 becomes 125/1000, which simplifies to 1/8. If you'd rather skip the manual simplification, Ihsabha's Percent to Fraction Calculator reduces any percentage or decimal to its simplest fraction instantly.
This is the simplest conversion of the three: multiply the decimal by 100, and add a percent sign.
In practice, multiplying by 100 just means moving the decimal point two places to the right — a shortcut worth memorizing since this conversion comes up constantly.
This reverses the previous conversion: divide the percentage by 100, which is the same as moving the decimal point two places to the left.
This exact conversion is the first step in almost every percentage formula covered elsewhere on this site — before you can multiply by a percentage, you generally need it in decimal form first.
There are two equally valid routes to convert a fraction directly to a percentage.
Both routes produce the identical answer — pick whichever feels more natural. Ihsabha's Fraction to Percent Calculator handles this conversion instantly if you'd rather skip the manual steps entirely. It's also worth reading Markup vs. Margin: How to Calculate Each Percentage Correctly if this situation applies to you.
To convert a percentage to a fraction, write it over 100 and simplify.
For percentages with a decimal point, like 12.5%, first eliminate the decimal by multiplying both the percentage and 100 by 10 (giving 125/1000), then simplify as usual to 1/8.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.3% |
| 2/3 | 0.666... | 66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
| 1/6 | 0.1666... | 16.7% |
| 1/100 | 0.01 | 1% |
Memorizing this short table covers the vast majority of conversions you'll ever need in daily life, from splitting a bill three ways to reading a nutrition label's percentages at a glance.
Fractions like 1/3, 1/6, 1/7, and 1/9 don't convert into decimals that end cleanly — they repeat forever. In practice, this is handled one of two ways: round to a sensible number of decimal places for everyday use (1/3 ≈ 0.33), or write the exact repeating pattern with a bar or ellipsis when precision matters (1/3 = 0.3̄, meaning the 3 repeats indefinitely). For most day-to-day purposes — splitting a bill, estimating a discount — two or three decimal places is more than accurate enough; the extra digits rarely change the practical outcome.
A mixed number like 2 1/4 converts the same way, just with an extra step: first convert it to an improper fraction (multiply the whole number by the denominator, add the numerator, keep the same denominator), then proceed as usual.
A percentage over 100%, like 225% here, is completely normal for a mixed number greater than 1 — it simply reflects that the value exceeds a single whole.
A handful of recurring errors account for most conversion mistakes: This naturally leads to a related question, answered in How to Calculate a Tip: The Complete Tip Percentage Guide. For an instant, practical check, the Fraction to Percent Calculator is ready to go.
Fluent conversion between these three formats shows up constantly outside school. A recipe might list ingredients as fractions (3/4 cup flour) while a food scale displays decimals (170 g), and a nutrition label expresses daily values as percentages. Financial and religious calculations lean on the same skill too — working out 2.5% Zakat on savings is far easier once you're comfortable converting that percentage to the decimal 0.025 first. Even reading a discount sign that says "1/3 off" requires converting it to 33.3% to compare it against a competing "30% off" sign at another store.
Rather than dividing from scratch every time, a handful of fraction-to-percentage conversions are worth memorizing outright, since they appear so often: halves (50%), quarters (25%, 50%, 75%), fifths (20%, 40%, 60%, 80%), and tenths (10% increments). Once these are second nature, most everyday fractions you encounter — in recipes, discounts, or survey results — can be converted at a glance without reaching for a calculator or working through the division step by step.
The same rules apply at either extreme, though it's worth seeing them worked out since the numbers can look unfamiliar. A very small percentage like 0.5% converts to the decimal 0.005 (divide by 100, moving the decimal two places left) and to the fraction 1/200 (0.5/100 = 5/1000, which simplifies to 1/200). A very large percentage like 350% converts to the decimal 3.5 and the improper fraction 7/2 (350/100 simplifies to 7/2). In both cases, the exact same division-by-100 and simplification steps from earlier in this guide apply without any modification — there's no separate rule needed just because the number is unusually small or large.
Before relying on a converted value for a recipe, a grade, or a shared document, a few quick sanity checks catch most errors:
| Situation | Original Format | Converted |
|---|---|---|
| Recipe scaled down | 3/4 cup flour | 0.75 cup / 75% of a full cup |
| Test score | 17/20 correct | 0.85 / 85% |
| Sale sign | "1/3 off" | 0.333 / 33.3% off |
| Survey result | 0.62 approval | 62% approval |
| Nisab-eligible Zakat rate | 2.5% | 0.025 / 1/40 |
Each row uses one of the direct conversion methods covered earlier in this guide — the format changes to suit the context, but the underlying value and the steps to convert it stay exactly the same. If you want to go further, How to Calculate Percentage Off: Discount & Sale Price Formula explains this point in more depth.
To see how all three formats connect, it helps to walk through a single real value end to end. Imagine a class where 21 out of 28 students passed an exam.
All three of these — 21/28, 3/4, 0.75, and 75% — describe the exact same pass rate. A teacher writing a report might use the percentage for clarity ("75% of the class passed"), a spreadsheet might store the decimal for calculations (0.75), and the original raw tally might be recorded as the fraction (21/28) before it was ever simplified. None of these is more "correct" than another; they're the same fact told three different ways, and being able to move fluently between them means you're never stuck depending on which format a particular source happens to use.
Although all three formats can represent the same value, precision can be lost in translation if you're not careful. A repeating decimal like 0.6667 is already a rounded approximation of the exact fraction 2/3; if that rounded decimal is used in a further calculation instead of the original fraction, small errors can accumulate, especially across multiple steps. For situations where exactness matters — splitting an inheritance, dividing ingredients precisely, or working through a multi-step calculation — it's often safer to keep values as fractions for as long as possible and only convert to a decimal or percentage at the very last step, right before presenting the final result.
Skip the manual arithmetic. Ihsabha's Fraction to Percent Calculator and Percent to Fraction Calculator handle every conversion in this guide instantly, including automatic simplification to the lowest terms.
Conversions are often just the first step before a larger percentage calculation. Once a value is in percentage form, Ihsabha's broader guide on how to calculate percentage covers finding a percentage of a number, or working out what percent one number is of another. And if you need to measure how much a value has grown or shrunk over time rather than convert a single static value, the dedicated guide to calculating percentage increase and decrease covers that calculation from the ground up.
Divide the numerator by the denominator to get a decimal, then multiply by 100. For example, 3/8 = 0.375, and 0.375 × 100 = 37.5%.
A fraction produces a repeating decimal when its denominator (in simplest form) has prime factors other than 2 or 5. Fractions like 1/3, 1/6, and 1/7 fall into this category and never terminate cleanly.
Write it over 100 (12.5/100), then multiply both the top and bottom by 10 to clear the decimal (125/1000), and simplify to its lowest terms — in this case, 1/8.
Yes. Any percentage over 100%, such as 150%, converts to an improper fraction greater than 1 — in this case, 150/100, which simplifies to 3/2.
Converting between fractions, decimals, and percentages is exact math with no inherent estimation, as long as repeating decimals are rounded consistently and fractions are fully simplified. The most common sources of error are a misplaced decimal point, an incompletely simplified fraction, or an overly aggressive rounding of a repeating decimal. With the core division-and-multiplication steps in this guide, and the reference table above for the values you'll use most often, you'll be able to move confidently between all three formats — whatever the situation calls for.
Work it out instantly with Ihsabha's Percentage Calculator and Percentage Change Calculator. For related reading on Ihsabha's blog, see How to Use a Scientific Calculator: Every Function Explained, Degrees vs. Radians: The Complete Guide to Angle Units and Significant Figures: Rules, Examples & How to Round Correctly.