Volver a lecciones

🔬 Notación Científica

Unidad Ciencias Naturales 9° Prof. Juan Diego Andrés Prada Ramírez
<div class="nc-example-box earth"> <div class="nc-ex-header">🤔 Imagina escribir...</div> <div class="nc-ex-emoji-row"> <span class="nc-orbit">🌍</span> <span style="font-size:1.5rem;opacity:.4;">↔️</span> <span class="nc-orbit" style="animation-delay:-.5s;">☀️</span> </div> <div class="nc-ex-number" style="color:#6c63ff;"> <span id="nc-earth-counter">0</span> <span style="font-size:.7em;opacity:.5;"> metros</span> </div> <div class="nc-ex-label">Distancia de la Tierra al Sol</div> </div> <div class="nc-example-box atom"> <div class="nc-ex-header">🔬 O escribir...</div> <div style="text-align:center;font-size:2rem;margin:.3rem 0;">⚛️</div> <div class="nc-ex-number" style="color:#00a88a;"> <span id="nc-atom-counter">1</span> <span style="font-size:.7em;opacity:.5;"> metros</span> </div> <div class="nc-ex-label">Diámetro de un átomo de hidrógeno</div> </div> <div class="nc-locura"> <span class="nc-explode">🤯</span> ¡Sería una locura usar todos esos ceros cada vez! <span class="nc-explode" style="animation-delay:-.5s;">🤯</span> </div> <div class="nc-definition"> <p>La <span class="nc-highlight">Notación Científica</span> es un atajo genial que expresa cualquier número como un valor <span class="nc-highlight">entre 1 y 10</span> multiplicado por una <span class="nc-highlight">potencia de 10</span>.</p> </div> <div class="nc-shortcut"> 🌍 <span class="nc-arrow">↔️</span> ☀️ = 1,4968 × 10<sup style="font-size:.6em;">11</sup> m </div> <h2 class="nc-rules-title">📐 Reglas Básicas</h2> <div class="nc-rules-grid"> <div class="nc-rule-card rule-big"> <div class="nc-rule-num">1</div> <div> <strong>Números mayores que 1</strong><br> Mueve la coma decimal hacia la <strong>izquierda</strong> hasta que quede un solo dígito entero. Las posiciones recorridas son el exponente <span class="nc-rule-pill pill-purple">positivo (+)</span><br> <span style="font-family:'JetBrains Mono',monospace;font-size:.85rem;opacity:.7;">86.000 → 8,6 × 10⁴</span> </div> </div> <div class="nc-rule-card rule-small"> <div class="nc-rule-num">2</div> <div> <strong>Números menores que 1</strong><br> Mueve la coma hacia la <strong>derecha</strong> hasta tener un dígito entre 1 y 9. Las posiciones recorridas son el exponente <span class="nc-rule-pill pill-green">negativo (−)</span><br> <span style="font-family:'JetBrains Mono',monospace;font-size:.85rem;opacity:.7;">0,00086 → 8,6 × 10⁻⁴</span> </div> </div> <div class="nc-rule-card rule-gold"> <div class="nc-rule-num">⭐</div> <div> <strong>La regla de oro</strong><br> El coeficiente <strong>siempre</strong> debe ser un número ≥ 1 y < 10. </div> </div> </div> <div class="nc-tip-card"> <div class="nc-tip-header">💡 Truco para Recordar</div> <div class="nc-tip-row"> <span class="nc-tip-arrow">📏</span> Número <strong>GRANDE</strong> <span class="nc-tip-arrow">→</span> exponente <span class="nc-tip-tag tag-pos">POSITIVO</span> <span style="opacity:.5;font-size:.8rem;">(coma se mueve a la izquierda)</span> </div> <div class="nc-tip-row"> <span class="nc-tip-arrow">🔍</span> Número <strong>PEQUEÑO</strong> <span class="nc-tip-arrow">→</span> exponente <span class="nc-tip-tag tag-neg">NEGATIVO</span> <span style="opacity:.5;font-size:.8rem;">(coma se mueve a la derecha)</span> </div> </div> <script> (function() { // Animación: Earth counter (0 → 149.680.000.000) var earthEl = document.getElementById('nc-earth-counter'); var atomEl = document.getElementById('nc-atom-counter'); if (!earthEl || !atomEl) return; var earthTarget = 149680000000; var earthDuration = 2000; // 2s var earthStart = Date.now(); function animEarth() { var elapsed = Date.now() - earthStart; var progress = Math.min(elapsed / earthDuration, 1); // Easing progress = 1 - Math.pow(1 - progress, 3); var val = Math.round(earthTarget * progress); earthEl.textContent = val.toLocaleString('es-CO'); if (progress < 1) requestAnimationFrame(animEarth); } // Animación: Atom counter (1 → 0,0000000002) var atomSteps = [ '1', '0,9', '0,5', '0,1', '0,05', '0,01', '0,005', '0,001', '0,0005', '0,0001', '0,00005', '0,00001', '0,000005', '0,000001', '0,0000005', '0,0000001', '0,00000005', '0,00000001', '0,000000005', '0,000000001', '0,0000000005', '0,0000000002' ]; var atomIdx = 0; var atomInterval; function animAtom() { if (atomIdx < atomSteps.length) { atomEl.textContent = atomSteps[atomIdx]; atomEl.style.transform = 'scale(1.05)'; setTimeout(function() { atomEl.style.transform = ''; }, 60); atomIdx++; } else { clearInterval(atomInterval); atomEl.style.color = '#00d4aa'; atomEl.style.textShadow = '0 0 10px rgba(0,212,170,.4)'; } } // Iniciar con un pequeño delay setTimeout(function() { animEarth(); atomInterval = setInterval(animAtom, 120); }, 400); })(); </script> --- ## 🎬 Animación: ¡Observa cómo se Mueve la Coma! Haz clic en un número para ver paso a paso cómo se convierte a notación científica. <div id="nc-anim-container"> <div id="nc-anim"> <div class="nc-btn-row"> <button class="nc-btn nc-btn-big" onclick="ncGo('86000')">86.000</button> <button class="nc-btn nc-btn-big" onclick="ncGo('4700000')">4.700.000</button> <button class="nc-btn nc-btn-big" onclick="ncGo('149680000000')">149.680.000.000</button> <button class="nc-btn nc-btn-small" onclick="ncGo('0.00086')">0,00086</button> <button class="nc-btn nc-btn-small" onclick="ncGo('0.0000032')">0,0000032</button> </div> <div class="nc-stage" id="nc-stage"> <div class="nc-placeholder-msg">☝️ Elige un número para ver la animación</div> </div> </div> </div> <script> (function() { var tmr = null; window.ncGo = function(numStr) { if (tmr) { clearInterval(tmr); tmr = null; } var stage = document.getElementById('nc-stage'); var num = parseFloat(numStr); var isBig = num >= 1; var rawDigits, commaPos; if (isBig) { rawDigits = numStr.split(''); commaPos = rawDigits.length; } else { var pts = numStr.split('.'); rawDigits = (pts[0]+pts[1]).split(''); commaPos = pts[0].length; } var firstSig = -1; for (var i=0;i<rawDigits.length;i++){if(rawDigits[i]!=='0'){firstSig=i;break;}} var targetComma=firstSig+1, totalSteps=Math.abs(commaPos-targetComma); var finalExp=isBig?totalSteps:-totalSteps; var lastSig=firstSig; for(var ls=rawDigits.length-1;ls>firstSig;ls--){if(rawDigits[ls]!=='0'){lastSig=ls;break;}} var coefParts=[];for(var c=firstSig;c<=lastSig;c++)coefParts.push(rawDigits[c]); var coefStr=coefParts[0]+(coefParts.length>1?','+coefParts.slice(1).join(''):''); stage.innerHTML='<div class="nc-digits-row" id="ncdr"></div><div class="nc-exp-row" id="ncer"><span class="nc-coef-val" id="nccv">&mdash;</span><span class="nc-times-val">&times;</span><span class="nc-ten-val">10</span><span class="nc-exp-val" id="ncev">0</span></div><div class="nc-step-info" id="ncsi"></div>'; var dr=document.getElementById('ncdr'),html=''; for(var k=0;k<rawDigits.length;k++){var cls=(k>=firstSig&&k<=lastSig)?'nc-digit sig':'nc-digit';html+='<span class="'+cls+'" id="ncd'+k+'">'+rawDigits[k]+'</span>';if(k+1===commaPos&&commaPos<rawDigits.length)html+='<span class="nc-comma-el" id="ncc">,</span>';} if(commaPos>=rawDigits.length)html+='<span class="nc-comma-el" id="ncc" style="opacity:0;width:0;">,</span>'; dr.innerHTML=html;var curComma=commaPos,step=0; var si=document.getElementById('ncsi'),cv=document.getElementById('nccv'),ev=document.getElementById('ncev'); si.innerHTML=isBig?'⬅️ La coma se moverá <strong>'+totalSteps+'</strong> posiciones a la izquierda':'➡️ La coma se moverá <strong>'+totalSteps+'</strong> posiciones a la derecha'; setTimeout(function(){var cc=document.getElementById('ncc');if(cc){cc.style.opacity='1';cc.style.width='';}},300); setTimeout(function(){ tmr=setInterval(function(){ if(step>=totalSteps){clearInterval(tmr);tmr=null;for(var f=0;f<rawDigits.length;f++){var dd=document.getElementById('ncd'+f);if(!dd)continue;if(f>=firstSig&&f<=lastSig){dd.className='nc-digit sig';dd.style.color='#fff';dd.style.textShadow='0 0 10px rgba(255,255,255,.4)';dd.style.transform='';}else{dd.className='nc-digit dim';}}cv.innerHTML=coefStr;cv.classList.add('nc-glow-anim');ev.innerHTML=finalExp;ev.classList.add('nc-glow-anim');si.innerHTML='✅ <strong>'+coefStr+' × 10<sup>'+finalExp+'</sup></strong> — exponente '+(isBig?'positivo porque el número es grande':'negativo porque el número es menor que 1');si.style.color='#00d4aa';return;} step++;var curExp=isBig?step:-step;var oldC=document.getElementById('ncc');if(oldC)oldC.remove();if(isBig){curComma--;}else{curComma++;} var passIdx=isBig?curComma:curComma-1;var pd=document.getElementById('ncd'+passIdx); if(pd){var isSigD=(passIdx>=firstSig&&passIdx<=lastSig);pd.classList.add('glow');(function(el,sig){setTimeout(function(){el.classList.remove('glow');if(!sig)el.classList.add('dim');else el.className='nc-digit sig';},350);})(pd,isSigD);} var nc=document.createElement('span');nc.className='nc-comma-el';nc.id='ncc';nc.textContent=',';var ref=document.getElementById('ncd'+curComma);if(ref)ref.parentNode.insertBefore(nc,ref); ev.innerHTML=(curExp>=0?'+':'')+curExp;ev.style.transform='scale(1.4)';setTimeout(function(){ev.style.transform='';},200); cv.innerHTML=step>=totalSteps-1?coefStr:'...'; si.innerHTML='📍 Paso '+step+' de '+totalSteps+' — exponente: <strong style="color:#ff6b9d;">10<sup>'+((curExp>=0?'+':'')+curExp)+'</sup></strong>'; },650); },800); }; })(); </script> --- ## Operaciones con Notación Científica No basta con saber escribir números; necesitas operar con ellos. ### ➕ Suma y Resta Los exponentes **deben ser iguales**. Si no lo son, ajusta uno de los dos. Luego suma o resta los coeficientes. $$2{,}4 \times 10^3 + 7{,}1 \times 10^3 = 9{,}5 \times 10^3$$ > ⚠️ **Error Común en Sumas** > > Nunca sumes directamente $4{,}7 \times 10^{18} + 6 \times 10^{19}$ sin igualar exponentes. > Debes convertir: $0{,}47 \times 10^{19} + 6 \times 10^{19} = 6{,}47 \times 10^{19}$ > ¡Igualar exponentes es OBLIGATORIO! <div id="nc-ops-container"> <div class="nc-op-box"> <div class="nc-op-title">🎬 Animación: Suma y Resta en Notación Científica</div> <div class="nc-btn-row"> <button class="nc-btn nc-btn-big" onclick="ncOp('sum',2.4,3,7.1,3)">2,4×10³ + 7,1×10³</button> <button class="nc-btn nc-btn-big" onclick="ncOp('sum',4.7,18,6,19)">4,7×10¹⁸ + 6×10¹⁹</button> <button class="nc-btn nc-btn-big" onclick="ncOp('sum',8.5,4,3.2,4)" style="background:linear-gradient(135deg,#ff6b9d,#e0557a);">8,5×10⁴ + 3,2×10⁴</button> <button class="nc-btn nc-btn-small" onclick="ncOp('sub',5.3,7,4.8,7)">5,3×10⁷ − 4,8×10⁷</button> <button class="nc-btn nc-btn-small" onclick="ncOp('sum',3.2,-4,5.8,-4)">3,2×10⁻⁴ + 5,8×10⁻⁴</button> </div> <div id="nc-sum-stage"><div class="nc-placeholder-msg">☝️ Elige una suma o resta</div></div> <div id="nc-sub-stage" style="display:none;"></div> </div> --- ### ✖️ Multiplicación Multiplica los coeficientes y **suma los exponentes**: $$(3 \times 10^5) \times (2 \times 10^8) = 6 \times 10^{13}$$ <div class="nc-op-box"> <div class="nc-op-title">🎬 Animación: Multiplicación en Notación Científica</div> <div class="nc-btn-row"> <button class="nc-btn nc-btn-big" onclick="ncOp('mul',3,5,2,8)">3×10⁵ × 2×10⁸</button> <button class="nc-btn nc-btn-big" onclick="ncOp('mul',4.5,3,2,7)">4,5×10³ × 2×10⁷</button> <button class="nc-btn nc-btn-small" onclick="ncOp('mul',6,-3,3,-4)">6×10⁻³ × 3×10⁻⁴</button> </div> <div id="nc-mul-stage"><div class="nc-placeholder-msg">☝️ Elige una multiplicación</div></div> </div> --- ### ➗ División Divide los coeficientes y **resta los exponentes**: $$\frac{8 \times 10^{-3}}{4 \times 10^2} = 2 \times 10^{-5}$$ <div class="nc-op-box"> <div class="nc-op-title">🎬 Animación: División en Notación Científica</div> <div class="nc-btn-row"> <button class="nc-btn nc-btn-big" onclick="ncOp('div',8,-3,4,2)">8×10⁻³ ÷ 4×10²</button> <button class="nc-btn nc-btn-big" onclick="ncOp('div',9,12,3,5)">9×10¹² ÷ 3×10⁵</button> <button class="nc-btn nc-btn-small" onclick="ncOp('div',4.8,6,1.6,2)">4,8×10⁶ ÷ 1,6×10²</button> </div> <div id="nc-div-stage"><div class="nc-placeholder-msg">☝️ Elige una división</div></div> </div> </div> <script> (function() { var opTmr = null; function fc(c) { var s = (c % 1 === 0) ? c.toString() : c.toFixed(4).replace(/0+$/, '').replace(/\.$/, ''); return s.replace('.', ','); } function fn(c, e) { return '<span class="c">' + fc(c) + '</span><span class="t"> × </span><span class="b">10</span><span class="e">' + e + '</span>'; } window.ncOp = function(type, c1, e1, c2, e2) { if (opTmr) { clearTimeout(opTmr); opTmr = null; } // sub uses sum stage var stageId = type === 'sub' ? 'nc-sum-stage' : 'nc-' + type + '-stage'; var stage = document.getElementById(stageId); var opSymbol = type === 'sum' ? '+' : type === 'sub' ? '−' : type === 'mul' ? '×' : '÷'; // PRECOMPUTE everything var targetExp, adjC1, adjC2, needsEqExp = false; var resC, resE, needsAdj, finalC, finalE; if (type === 'sum' || type === 'sub') { targetExp = Math.max(e1, e2); adjC1 = c1 * Math.pow(10, e1 - targetExp); adjC2 = c2 * Math.pow(10, e2 - targetExp); adjC1 = parseFloat(adjC1.toPrecision(6)); adjC2 = parseFloat(adjC2.toPrecision(6)); needsEqExp = (e1 !== e2); resC = type === 'sub' ? parseFloat((adjC1 - adjC2).toPrecision(4)) : parseFloat((adjC1 + adjC2).toPrecision(4)); resE = targetExp; } else if (type === 'mul') { adjC1 = c1; adjC2 = c2; resC = parseFloat((c1 * c2).toPrecision(4)); resE = e1 + e2; } else { adjC1 = c1; adjC2 = c2; resC = parseFloat((c1 / c2).toPrecision(4)); resE = e1 - e2; } needsAdj = (Math.abs(resC) >= 10 || (Math.abs(resC) < 1 && Math.abs(resC) > 0)); finalC = resC; finalE = resE; if (Math.abs(resC) >= 10) { finalC = parseFloat((resC / 10).toPrecision(4)); finalE = resE + 1; } else if (Math.abs(resC) < 1 && Math.abs(resC) > 0) { finalC = parseFloat((resC * 10).toPrecision(4)); finalE = resE - 1; } // Build HTML stage.innerHTML = '<div class="nc-op-line">' + fn(c1, e1) + '</div>' + '<div class="nc-op-line"><span class="op">' + opSymbol + '</span></div>' + '<div class="nc-op-line" id="' + type + 'L2">' + fn(c2, e2) + '</div>' + '<div style="border-top:2px dashed rgba(255,255,255,.1);margin:.6rem 0;"></div>' + '<div class="nc-op-steps-log" id="' + type + 'Log"></div>' + '<div class="nc-op-result" id="' + type + 'Res"></div>'; var log = document.getElementById(type + 'Log'); var res = document.getElementById(type + 'Res'); // Build steps array — each step adds a line to the log var steps = []; if (type === 'sum' || type === 'sub') { var opWord = type === 'sub' ? 'Restamos' : 'Sumamos'; var opSym = type === 'sub' ? ' − ' : ' + '; // Step 1: Check exponents if (needsEqExp) { steps.push('❌ Exponentes diferentes: <strong>' + e1 + '</strong> ≠ <strong>' + e2 + '</strong>'); var fixedLine = (e1 < e2) ? 1 : 2; var adjVal = (fixedLine === 1) ? adjC1 : adjC2; steps.push('🔄 Igualamos → ' + fc(fixedLine === 1 ? c1 : c2) + '×10<sup>' + (fixedLine === 1 ? e1 : e2) + '</sup> se convierte en <strong style="color:#6c63ff;">' + fc(adjVal) + '×10<sup>' + targetExp + '</sup></strong>'); } else { steps.push('✅ Exponentes iguales: ambos son 10<sup>' + e1 + '</sup>'); } // Step 2: Sum/Sub coefs steps.push((type === 'sub' ? '➖' : '➕') + ' ' + opWord + ' coeficientes: ' + fc(adjC1) + opSym + fc(adjC2) + ' = <strong style="color:#6c63ff;">' + fc(resC) + '</strong>'); } else if (type === 'mul') { steps.push('✖️ Multiplicamos coeficientes: ' + fc(c1) + ' × ' + fc(c2) + ' = <strong style="color:#6c63ff;">' + fc(resC) + '</strong>'); steps.push('➕ Sumamos exponentes: ' + e1 + ' + (' + e2 + ') = <strong style="color:#ff6b9d;">' + resE + '</strong>'); } else { steps.push('➗ Dividimos coeficientes: ' + fc(c1) + ' ÷ ' + fc(c2) + ' = <strong style="color:#6c63ff;">' + fc(resC) + '</strong>'); steps.push('➖ Restamos exponentes: (' + e1 + ') − (' + e2 + ') = <strong style="color:#ff6b9d;">' + resE + '</strong>'); } // Step 3: intermediate result steps.push('🎯 Resultado parcial: <strong>' + fc(resC) + ' × 10<sup>' + resE + '</sup></strong>'); // Step 4: Adjust if needed (in NC the coef must be 1 ≤ c < 10) if (needsAdj) { if (Math.abs(resC) >= 10) { steps.push('⚠️ <strong style="color:#ff6b9d;">' + fc(resC) + ' ≥ 10</strong> — en notación científica el coeficiente debe ser entre 1 y 10'); steps.push('🔄 Corremos la coma a la izquierda → coeficiente: <strong style="color:#6c63ff;">' + fc(finalC) + '</strong>, exponente sube a <strong style="color:#ff6b9d;">' + finalE + '</strong>'); } else { steps.push('⚠️ <strong style="color:#ff6b9d;">' + fc(resC) + ' < 1</strong> — en notación científica el coeficiente debe ser entre 1 y 10'); steps.push('🔄 Corremos la coma a la derecha → coeficiente: <strong style="color:#6c63ff;">' + fc(finalC) + '</strong>, exponente baja a <strong style="color:#ff6b9d;">' + finalE + '</strong>'); } } // Final step steps.push('FINAL'); // Execute with timing var si = 0; function addStep() { if (si >= steps.length) return; var text = steps[si]; // Mark previous steps as done var prevSteps = log.querySelectorAll('.nc-op-step'); prevSteps.forEach(function(s) { s.classList.remove('step-active'); s.classList.add('step-done'); }); if (text === 'FINAL') { // Show final result res.innerHTML = fn(finalC, finalE); res.classList.add('nc-glow-anim'); var fStep = document.createElement('div'); fStep.className = 'nc-op-step step-final'; fStep.innerHTML = '✅ Resultado: <strong>' + fc(finalC) + ' × 10<sup>' + finalE + '</sup></strong>'; log.appendChild(fStep); return; } // Update the adjusted line visually (for sum) if (type === 'sum' && needsEqExp && si === 1) { var l2 = document.getElementById(type + 'L2'); if (e1 < e2) { // line1 needs adjustment — but we only have L2 reference, reconstruct } } var step = document.createElement('div'); step.className = 'nc-op-step step-active'; step.innerHTML = text; log.appendChild(step); si++; opTmr = setTimeout(addStep, 1300); } // Start after a small delay opTmr = setTimeout(addStep, 500); }; })(); </script> --- ## 🎮 Practica: Convierte tú mismo <div id="nc-practice-container"> <div id="nc-practice"> <div class="nc-pq" id="ncpq">Cargando...</div> <div class="nc-pi"> <input type="text" id="ncpc" placeholder="Coef." style="width:80px;"> <span style="font-size:1.2rem;color:#ffd700;">&times; 10</span> <input type="text" id="ncpe" placeholder="exp" class="nc-sup-input" style="width:50px;border-color:#ff6b9d;font-size:.85rem;"> <button class="nc-pc" onclick="ncPChk()">Verificar</button> </div> <div class="nc-pf" id="ncpf"></div> <button class="nc-pn" onclick="ncPN()">Nuevo número →</button> </div> </div> <script> (function(){ var pC=null,pE=null; function gen(){var big=Math.random()>.4;if(big){var e=Math.floor(Math.random()*8)+2;var c=parseFloat((Math.random()*8.5+1.1).toFixed(1));return{num:c*Math.pow(10,e),coef:c,exp:e};}else{var en=-(Math.floor(Math.random()*6)+1);var cn=parseFloat((Math.random()*8.5+1.1).toFixed(1));return{num:cn*Math.pow(10,en),coef:cn,exp:en};}} window.ncPN=function(){var d=gen();pC=d.coef;pE=d.exp;var display;if(d.num>=1)display=Math.round(d.num).toLocaleString('es-CO');else display=d.num.toFixed(Math.abs(pE)+1).replace('.',',');document.getElementById('ncpq').textContent='\u{1F4DD} Expresa: '+display;document.getElementById('ncpf').innerHTML='';document.getElementById('ncpc').value='';document.getElementById('ncpe').value='';}; window.ncPChk=function(){var fb=document.getElementById('ncpf');var ca=parseFloat(document.getElementById('ncpc').value.replace(',','.'));var ea=parseInt(document.getElementById('ncpe').value);if(isNaN(ca)||isNaN(ea)){fb.innerHTML='<span style="color:#ff6b9d;">\u26A0\uFE0F Escribe coeficiente y exponente</span>';return;}if(Math.abs(ca-pC)<.15&&ea===pE)fb.innerHTML='<span style="color:#00d4aa;font-size:1.2rem;">\u{1F389} \u00A1Correcto! '+pC+' \u00D7 10<sup>'+pE+'</sup></span>';else fb.innerHTML='<span style="color:#ff6b9d;">\u274C Respuesta: '+pC+' \u00D7 10<sup>'+pE+'</sup></span>';}; setTimeout(ncPN,200); })(); </script> --- ## Reto: La Vía Láctea Un año luz ≈ $9{,}4608 \times 10^6$ km. La Vía Láctea mide ≈ 100.000 años luz de diámetro. $$D = (9{,}4608 \times 10^6) \times (1 \times 10^5) = 9{,}4608 \times 10^{11} \text{ km}$$ ¡Casi un billón de kilómetros! La notación científica es la única forma razonable de escribir esto.