Volver a lecciones
🔬 Notación Científica
<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">—</span><span class="nc-times-val">×</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;">× 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='';};
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## 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.