½, 0.5 and 50% look like three different things. They're not. They're the same value, dressed three different ways — and learning to switch the outfit on the fly is a quiet little superpower.
Start hereWhen you write ½, 0.5 and 50%, you are pointing at the exact same amount three times. It's like a person in a hoodie, a ballgown and a swimsuit — different costumes, but underneath, it's one and the same value.
So why bother with three? Because each costume is good for a different job. A fraction shows the recipe — how many equal pieces, and how many you took. A decimal slots neatly into a calculator and lines up for adding. A percentage says "out of 100," which makes comparing painless. The skill this page hands you isn't memorising a table — it's being able to change the costume whenever the job changes. Get that, and a whole shelf of "hard" maths quietly stops being hard.
Let's get the words straight first, because once you can name the parts, everything afterwards feels easier. Take a pizza cut into two equal slices, and you grab one.
A fraction writes that as ½. The bottom number, the denominator, says how many equal pieces the whole was cut into — here, 2. The top number, the numerator, says how many of those pieces you have — here, 1. So ½ literally reads "one out of two equal pieces." A fraction is a recipe for sharing.
A decimal writes the same amount as 0.5. Decimals use place value — the spots after the dot mean tenths, hundredths, thousandths — so 0.5 means "five tenths," which is exactly half. Decimals are the costume your calculator likes best, because they slide straight into adding, subtracting and comparing.
A percentage writes it as 50%. The little % sign is just shorthand for "out of 100" (per cent is old language for "per hundred"). So 50% means "50 out of every 100" — and 50 out of 100 is, once again, half. Percentages are the costume for comparing, because everything is measured against the same fixed total of 100.
½ = 0.5 = 50%. Three spellings of one idea: half of the whole.
Two values that point at the same amount are called equivalent — they're equal in worth even though they're written differently. The rest of this page is really one question asked over and over: given one costume, how do you work out the other two?
There are three little rules, and that's the whole toolkit. Learn these and you can travel between any two forms.
Fraction → Decimal: divide the top by the bottom. A fraction bar is secretly a division sign. So ½ means "1 divided by 2," and 1 ÷ 2 = 0.5. Want ¾ as a decimal? Do 3 ÷ 4 = 0.75. The numerator goes into the calculator first, the denominator second.
Decimal → Percent: multiply by 100. Because a percentage is just "out of 100," you scale the decimal up to that total. The quick trick: the decimal point hops two places to the right. So 0.5 → 50%, and 0.75 → 75%. (Going the other way, percent → decimal, the point hops two places left: 25% → 0.25.)
Percent → Fraction: put it over 100, then simplify. Since a percentage already means "out of 100," you write it as a fraction with 100 on the bottom, then tidy it up. So 50% = 50/100, and you simplify — divide top and bottom by the same number until it can't shrink any more — to get ½. Likewise 25% = 25/100 = ¼.
Notice they form a little loop: fraction → decimal → percent → fraction. In the demo below you don't have to do any of the arithmetic by hand — but every number on screen is following exactly these three rules, so watch them happen live.
This is the heart of the page. Type into any one of the three boxes — the fraction, the decimal or the percent — and watch the other two change to match, instantly. The 100-square grid below fills to show the value, so you can see that all three costumes really are the same amount. Or just tap a quick-pick to load a famous one.
The grid has 100 squares, so it's really a percentage you can touch: fill 50 squares and you've shaded half of it. When a value doesn't land on a whole number of squares, watch the last square fill only part-way — that's a repeating decimal warning you it isn't exact.
A handful of these come up so often that it's worth recognising them on sight — the way you just know that 5 + 5 is 10 without thinking. Here are the friendliest fractions in all three costumes. Try typing them into the converter above and watch the grid agree.
Look at how the patterns hum once you see them. Halves, quarters and fifths all turn into clean, tidy decimals and round percentages — because their denominators (2, 4, 5) get along nicely with the way decimals are built out of tenths and hundredths. ⅓ is the odd one out, and the table flags it honestly: its decimal and percentage are marked approximate, because they never quite stop. We'll meet that troublemaker properly in a moment.
A small confidence-builder: ¾ is the same as 0.75 is the same as 75%, so if a quiz shows you "0.75 of the class passed," your brain can quietly translate that to "three-quarters" or "75 out of 100" — whichever picture helps you most. That freedom to re-dress a number is exactly what fluency feels like.
Here's a real situation. You sit three quizzes and you want to know which one you actually did best on:
Staring at 17/20, 21/25 and 0.82, you genuinely can't tell at a glance — they're three different costumes, measured against three different totals. So put them all in the same outfit: percentages, where everything is measured out of the same 100.
17/20 is 17 ÷ 20 = 0.85 = 85%. 21/25 is 21 ÷ 25 = 0.84 = 84%. And 0.82 is just 82%. Now the ranking is obvious: Quiz A (85%) beat Quiz B (84%) by a whisker, and both beat Quiz C. The numbers didn't change — you just dressed them all the same so they could line up fairly. That is the everyday magic of percentages: a common total of 100 turns "apples vs oranges" into a simple race.
This is why shops, news reports and sports stats all lean on percentages. "37 out of 50 people agreed" is fiddly; "74% agreed" is instant. Whenever you need to compare things of different sizes, the percentage costume is almost always the one to reach for.
Most friendly fractions turn into short, polite decimals. ⅓ does not. Try the division: 1 ÷ 3 = 0.3333… and those 3s march on forever. A decimal whose digits repeat without ever ending is called a repeating decimal (your teacher might say recurring). It's not broken and it's not a mistake — it's just what happens when 3 refuses to divide evenly into 1.
So how do we write it down without an infinitely long pencil? We round — we chop it off at a sensible spot and accept we're a hair away from the true value. Rounded, ⅓ ≈ 0.333, and as a percentage ⅓ ≈ 33.3%. That little ≈ sign means "approximately equal," and it's doing important, honest work: it's admitting "this is close, but not exact." The exact value is still the fraction ⅓ — fractions can hold the repeating value perfectly, which is one more reason they're worth keeping around.
⅓ = 0.333… ≈ 0.333, and ⅓ ≈ 33.3%. The fraction is exact; the rounded decimal and percent are only close — so we mark them with ≈.
You can feel this in the converter's grid. Type ⅓ (or tap its quick-pick) and the grid fills 33 whole squares — then the 34th square fills only about a third of the way, because the value lands between squares. That stubborn part-filled square is the repeating decimal, made visible. A neat check: 0.333 + 0.333 + 0.333 = 0.999, just shy of 1, even though ⅓ + ⅓ + ⅓ is exactly 1. The missing sliver is precisely what rounding threw away.
The takeaway is gentle but important: when a decimal or percent is rounded, say so. Writing "33.3%" is fine and useful — just don't pretend it's the whole truth. The honest version always carries that ≈.
It's the single most common slip, and it's an easy one to make: you see 0.5, you spot a 5, and your brain blurts out "5%." But 0.5 is 50%, not 5%. The two are ten times apart, and that's a difference that can wreck a calculation — imagine a 50%-off sale ringing up as 5% off.
Grabbing the digit and gluing a % sign on. It ignores the one rule that matters: turning a decimal into a percent means multiplying by 100, not just reading off the figure.
The point hops two places right: 0.5 → 50%. To actually get 5% you'd need 0.05, because 0.05 × 100 = 5. The number of zeros really matters.
Lock in the pattern with a quick ladder: 0.5 = 50%, 0.05 = 5%, 0.005 = 0.5%. Each time you tuck another zero in behind the point, the percentage shrinks by a factor of ten. So before you slap a % sign on a decimal, do the two-place hop every single time — it costs you half a second and saves you from the most popular mistake in the whole topic.
Each fraction on the left has exactly one partner on the right — its equal value, written as a decimal or a percentage. Tap a fraction, then tap the card you think matches it. Get it right and the pair locks in pink; get it wrong and they'll wobble so you can try again. Find all five.
Watch out for ⅓ — its partner is marked ≈33.3%, because (you guessed it) the exact decimal never stops. Matching it means trusting that "approximately a third" really is the same value in a rounded coat.
No pressure and no score kept — just pick the answer you believe, and the reason will appear so you can check your thinking. If one trips you up, scroll back up and try it in the converter.
½, 0.5 and 50% are the same amount written three ways. Pick the costume that suits the job.
Fraction → decimal: divide top by bottom. Decimal → percent: ×100. Percent → fraction: over 100, then simplify.
Some decimals repeat forever, like ⅓ = 0.333… If you round it, mark it with ≈ — close isn't the same as exact.