Fraction · decimal · percent

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#486f9d}.equation{display:flex;align-items:center;gap:23px;margin:22px 0 12px}.equation>div{flex:1;min-width:0}.equation b{display:block;font-size:clamp(24px,3.5vw,40px);font-variant-numeric:tabular-nums;overflow-wrap:anywhere;margin:10px 0}.equation>span{font-size:24px;color:#6581a4}.equation small{display:block;font-size:13px}@media(max-width:720px){.equation{gap:12px}.equation b{font-size:25px}}@media(max-width:540px){.equation{display:block}.equation>span{display:block;margin:10px 0}.equation b{margin:5px 0;font-size:32px}}</style></head><body style="--bg:#eef3f9;--accent:#3b6494"><main><header><div class="kicker">Number workshop</div><h1>Fraction · decimal · percent</h1><p class="muted">Convert one exact value into three forms, with rounding clearly marked.</p></header><section id="result" class="surface number-result" aria-live="polite"><div class="kicker">Same value · three representations</div><div class="equation"><div><small>Reduced fraction · exact</small><b id="fraction"></b></div><span>=</span><div><small>Decimal</small><b id="decimalResult"></b><small id="decimalStatus"></small></div><span>=</span><div><small>Percent</small><b id="percentResult"></b><small id="percentStatus"></small></div></div></section><p id="error" class="error" role="alert"></p><form id="form" class="panel" novalidate><label for="mode">Input form<select id="mode"><option value="fraction">Fraction</option><option value="decimal">Decimal</option><option value="percent">Percent</option></select></label><div id="fractionFields" class="row" style="margin-top:18px"><label for="numerator">Numerator · signed integer<input id="numerator" value="3" autocomplete="off"></label><label for="denominator">Denominator · nonzero signed integer<input id="denominator" value="8" autocomplete="off"></label></div><div id="valueField" hidden style="margin-top:18px"><label for="value">Decimal or percent number · no % symbol<input id="value" value="25" autocomplete="off"></label></div><div class="actions"><button>Convert value</button><button type="button" id="thirds" class="secondary">Try 2/3</button><button type="button" id="percent25" class="secondary">Try 25%</button><button type="button" id="decimal25" class="secondary">Try decimal 25</button></div></form><section class="panel"><h2>Conversion record</h2><pre id="trace"></pre></section><details><summary>Precision and input rules</summary><p>Fraction components are signed integers with magnitude at most 10,000. Decimal and percent entries are signed dot-decimal numbers with magnitude at most 10,000 and up to six decimal places. Leading digits are required. Blank values, commas, scientific notation, mixed numbers, and repeating notation are rejected.</p><p>The reduced fraction remains exact. Decimal and percent displays use at most six decimal places, rounding ties away from zero. Approximate outputs are labeled separately. A percent is a value divided by 100; values above 100% are allowed. No rounded output is reused for a calculation.</p></details><footer>Local session only. Nothing is sent, saved, approved, or submitted. Keep maintained source records authoritative.</footer></main><script>const $=id=>document.getElementById(id);const esc=s=>String(s).replace(/[&<>"']/g,c=>({'&':'&amp;','<':'&lt;','>':'&gt;','"':'&quot;',"'":'&#39;'}[c]));const money=n=>'$'+n.toFixed(2);

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function integer(s){if(!/^[+-]?[0-9]+$/.test(s)||s.length>12||Math.abs(Number(s))>10000)throw Error('Enter signed integers with magnitude at most 10,000.');return BigInt(s)}
function parse(mode,a,b){if(mode==='fraction')return rational(integer(a),integer(b));if(!['decimal','percent'].includes(mode))throw Error('Select a supported input form.');if(!/^[+-]?[0-9]+(?:[.][0-9]{1,6})?$/.test(a)||a.length>18||Math.abs(Number(a))>10000)throw Error('Enter a signed dot-decimal value, up to six places and magnitude 10,000.');const negative=a.startsWith('-'),s=a.replace(/^[+-]/,''),[x,y='']=s.split('.');return rational(BigInt(x+y)*(negative?-1n:1n),10n**BigInt(y.length)*(mode==='percent'?100n:1n))}
function display(r,mult=1n){const n=r.n*mult,abs=n<0n?-n:n,scale=1000000n,q=(abs*scale*2n+r.d)/(2n*r.d),digits=q.toString().padStart(7,'0'),s=(digits.slice(0,-6)+'.'+digits.slice(-6)).replace(/0+$/,'').replace(/[.]$/,'');return {text:(n<0n&&q?'-':'')+s,exact:abs*scale%r.d===0n}}
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$('form').addEventListener('submit',e=>{e.preventDefault();run()});['numerator','denominator','value'].forEach(x=>$(x).addEventListener('input',clear));$('mode').addEventListener('change',mode);$('thirds').onclick=()=>{$('mode').value='fraction';mode();$('numerator').value='2';$('denominator').value='3';run()};function sample(m){$('mode').value=m;mode();$('value').value='25';run()}$('percent25').onclick=()=>sample('percent');$('decimal25').onclick=()=>sample('decimal');run();</script>
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