A powers-of-ten explainer shows 10, 100, and 1000. The useful question is how many powers of ten separate the value from one, rather than how many digits happen to appear in its label.
Math.log10 answers that exponent question. For 1000, the result is 3 because ten cubed equals 1000. The example keeps the original value visible so the exponent remains tied to a concrete number.
Try the working example
Use Changed data to compare another sample, or edit the JSON and choose Update preview. Original data restores the starting case.
Live exampletry it here, then copy the code
<!doctype html><html lang="en"><head><meta charset="utf-8"><meta name="nos-demo-layout" content="responsive-lab"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Powers-of-ten explorer</title><style>*{box-sizing:border-box}body{margin:0;background:#edf1f0;color:#172d36;font:15px/1.5 system-ui,sans-serif}main{max-width:1040px;margin:auto;padding:24px}header{display:flex;justify-content:space-between;gap:12px;align-items:center;margin-bottom:20px}.eyebrow{font-size:11px;font-weight:800;letter-spacing:2px;color:#55716b;text-transform:uppercase}h1{font-size:clamp(23px,4vw,34px);line-height:1.15;margin:8px 0}h2{font-size:16px;margin:0 0 12px}.tag{border:1px solid #bfceca;border-radius:99px;padding:6px 12px;font-size:12px;white-space:nowrap}.panel{background:white;border:1px solid #d4dfdb;border-radius:18px;padding:20px;margin-bottom:14px;box-shadow:0 9px 30px #1d393407}.grid{display:grid;grid-template-columns:1fr 1fr;gap:14px}.result{background:#17352f;color:#f7fffb}.result h2{color:#c9ded5}.cards{display:grid;gap:10px;grid-template-columns:repeat(auto-fit,minmax(135px,1fr))}.card{background:#f2ffc2;color:#17352f;padding:15px;border-radius:12px;min-width:0;overflow-wrap:anywhere}.card small{display:block;color:#536f60;font-size:11px;font-weight:700;text-transform:uppercase;margin-bottom:4px}.field{display:block;margin:8px 0}.field small{margin:0 0 3px;text-transform:none}.value{font-size:15px;font-weight:650;white-space:pre-wrap}.hero{font-size:clamp(28px,5vw,46px);font-weight:750;line-height:1.2;overflow-wrap:anywhere}.muted{color:#587169;font-size:13px}.result .muted{color:#bed7cb}pre{margin:0;white-space:pre-wrap;overflow-wrap:anywhere;font:13px/1.6 ui-monospace,monospace;max-height:220px;overflow:auto}.toolbar{display:flex;flex-wrap:wrap;gap:8px;margin:12px 0}button{background:#17352f;color:white;border:0;border-radius:10px;padding:10px 14px;font:600 13px system-ui;cursor:pointer}button.secondary{background:#edf3ea;color:#244337;border:1px solid #d0ddd0}button:hover{filter:brightness(.94)}button:focus-visible,textarea:focus-visible,summary:focus-visible{outline:3px solid #749919;outline-offset:3px}textarea{display:block;width:100%;height:126px;border:1px solid #bccfc5;border-radius:10px;background:#fafcf9;padding:12px;font:13px/1.5 ui-monospace,monospace;resize:vertical;color:#15362c}label{font-weight:650;font-size:13px}details{margin-top:16px}summary{cursor:pointer;font-size:13px;font-weight:650}#status{min-height:20px;font-size:12px;color:#526f60;margin-top:8px}.error{color:#ffcfbf}.footer{font-size:12px;color:#627b72;margin-top:16px}.empty{font-size:18px;color:#c7dacd}.source-card{background:#f4f7f3;border:1px solid #dbe4d8;border-radius:10px;padding:12px;overflow-wrap:anywhere;white-space:pre-wrap}.source-list{display:flex;flex-wrap:wrap;gap:8px;max-height:170px;overflow:auto}.source-list .source-card{flex:1;min-width:100px}.code{background:#f5f8f2}mark{background:#f2ffc2;color:#183a2d;padding:2px 5px;border-radius:4px}@media(max-width:620px){main{padding:15px}.grid{grid-template-columns:1fr}.panel{padding:16px}header{align-items:flex-start}.tag{display:none}h1{font-size:25px}.cards{grid-template-columns:repeat(auto-fit,minmax(125px,1fr))}.source-list{max-height:120px}pre{max-height:150px}}</style></head><body><main>
<header><div><div class="eyebrow">JavaScript • Math log10</div><h1>Powers-of-ten explorer</h1><div class="muted">Change the data. See the actual result.</div></div><span class="tag">Interactive prototype</span></header>
<section class="panel"><label for="input">Input data (JSON)</label><textarea id="input" maxlength="10000" spellcheck="false"></textarea><div class="toolbar"><button id="run" type="button">Update preview</button><button class="secondary" id="original" type="button">Original data</button><button class="secondary" id="changed" type="button">Changed data</button><button class="secondary" id="edge" type="button">Empty / zero case</button></div><div id="status" role="status" aria-live="polite"></div></section>
<div class="grid"><section class="panel"><h2>Source after the operation</h2><div id="source" class="source-list"></div><p id="source-status" class="muted"></p></section><section class="panel result"><h2>Returned result</h2><div id="result" aria-live="polite"></div></section></div><details class="panel code"><summary>Inspect the exact values</summary><pre id="inspect"></pre></details>
<p class="footer">Local sample data only. No server request, account, or installation is needed.</p></main><script>
'use strict';
const initial = "1000";
const alternate = "1001";
const empty = "0";
const input = document.getElementById('input');
const output = document.getElementById('result');
const source = document.getElementById('source');
const status = document.getElementById('status');
function transform(data) { return Math.log10(data); }
function readable(value) {
if (value === undefined) return 'undefined';
if (typeof value === 'number' && Object.is(value, -0)) return '-0';
return JSON.stringify(value, (_, v) => typeof v === 'number' && !Number.isFinite(v) ? String(v) : v, 2);
}
function renderCards(value, host) {
host.replaceChildren();
if (Array.isArray(value)) {
if (!value.length) {const p=document.createElement('p');p.className='empty';p.textContent='No items returned';host.append(p);return;}
const grid=document.createElement('div');grid.className='cards';
value.slice(0,40).forEach((item,index)=>{const card=document.createElement('div');card.className='card';const label=document.createElement('small');label.textContent='Item '+(index+1);card.append(label);appendValue(item,card);grid.append(card);});host.append(grid);
if(value.length>40){const p=document.createElement('p');p.textContent='Showing 40 of '+value.length+' items.';host.append(p);}
} else if(value && typeof value==='object'){const card=document.createElement('div');card.className='card';appendValue(value,card);host.append(card);}
else {const p=document.createElement('div');p.className='hero';p.textContent=typeof value==='boolean'?(value?'Yes · true':'No · false'):value===undefined?'No value · undefined':value===''?'Empty string':String(value);host.append(p);}
}
function appendValue(value,host){
if(value && typeof value==='object' && !Array.isArray(value))Object.entries(value).slice(0,40).forEach(([key,item])=>{const row=document.createElement('div');row.className='field';const label=document.createElement('small');label.textContent=key;const text=document.createElement('span');text.className='value';text.textContent=typeof item==='string'?item:readable(item);row.append(label,text);host.append(row);});
else {const text=document.createElement('div');text.className='value';text.textContent=typeof value==='string'?value:readable(value);host.append(text);}
}
function update(){
try{
if(input.value.length>10000)throw new Error('Keep this sample below 10,000 characters.');
const data=JSON.parse(input.value);const before=readable(data);const result=transform(data);const after=readable(data);
renderCards(result,output);source.replaceChildren();(Array.isArray(data)?data.slice(0,40):[data]).forEach(item=>{const card=document.createElement('div');card.className='source-card';card.textContent=typeof item==='string'?item:readable(item);source.append(card);});document.getElementById('source-status').textContent=before===after?'Data values unchanged':'Data values changed in place';document.getElementById('inspect').textContent='Input before:\n'+before+'\n\nReturned result:\n'+readable(result)+'\n\nSource after:\n'+after;
output.classList.remove('error');status.textContent='Preview updated. '+(before===after?'Data values unchanged.':'Source data changed in place.');
}catch(error){output.replaceChildren();output.classList.add('error');output.textContent=error.name+': '+error.message;source.replaceChildren();document.getElementById('source-status').textContent='';document.getElementById('inspect').textContent='';status.textContent='Check the JSON and the input shape. Restore Original data to start again.';}
}
document.getElementById('run').addEventListener('click',update);
[['original',initial],['changed',alternate],['edge',empty]].forEach(([id,value])=>document.getElementById(id).addEventListener('click',()=>{input.value=value;update();}));
input.value=initial;update();
</script></body></html>
Turn a positive value into a base-ten exponent
Math.log10(data) calculates the base-ten logarithm. Exact powers such as 10, 100, and 1000 correspond to exponents 1, 2, and 3. One corresponds to zero because 10 raised to zero equals 1.
Values between powers return fractional exponents. A value of 500 lies between 100 and 1000, so its exponent lies between 2 and 3. You can use that continuous scale in a numeric explainer without pretending the value is an exact power of ten.
The source number is not changed. Use the result as an exponent or scale coordinate, and retain the original value for labels and interpretation.
const data = 1000;
const result = Math.log10(data);
console.log(result);
The original sample returns:
3
Keep the example on your own page
The smaller version below includes the HTML, styles, and script. Choose Copy code, save the result as an index.html file, and open it in a browser.
Live exampletry it here, then copy the code
<!doctype html><html lang="en"><head><meta charset="utf-8"><meta name="nos-demo-layout" content="responsive-lab"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Powers-of-ten explorer</title><style>*{box-sizing:border-box}body{margin:0;background:#edf1f0;color:#172d36;font:15px/1.5 system-ui,sans-serif}main{max-width:1040px;margin:auto;padding:24px}header{display:flex;justify-content:space-between;gap:12px;align-items:center;margin-bottom:20px}.eyebrow{font-size:11px;font-weight:800;letter-spacing:2px;color:#55716b;text-transform:uppercase}h1{font-size:clamp(23px,4vw,34px);line-height:1.15;margin:8px 0}h2{font-size:16px;margin:0 0 12px}.tag{border:1px solid #bfceca;border-radius:99px;padding:6px 12px;font-size:12px;white-space:nowrap}.panel{background:white;border:1px solid #d4dfdb;border-radius:18px;padding:20px;margin-bottom:14px;box-shadow:0 9px 30px #1d393407}.grid{display:grid;grid-template-columns:1fr 1fr;gap:14px}.result{background:#17352f;color:#f7fffb}.result h2{color:#c9ded5}.cards{display:grid;gap:10px;grid-template-columns:repeat(auto-fit,minmax(135px,1fr))}.card{background:#f2ffc2;color:#17352f;padding:15px;border-radius:12px;min-width:0;overflow-wrap:anywhere}.card small{display:block;color:#536f60;font-size:11px;font-weight:700;text-transform:uppercase;margin-bottom:4px}.field{display:block;margin:8px 0}.field small{margin:0 0 3px;text-transform:none}.value{font-size:15px;font-weight:650;white-space:pre-wrap}.hero{font-size:clamp(28px,5vw,46px);font-weight:750;line-height:1.2;overflow-wrap:anywhere}.muted{color:#587169;font-size:13px}.result .muted{color:#bed7cb}pre{margin:0;white-space:pre-wrap;overflow-wrap:anywhere;font:13px/1.6 ui-monospace,monospace;max-height:220px;overflow:auto}.toolbar{display:flex;flex-wrap:wrap;gap:8px;margin:12px 0}button{background:#17352f;color:white;border:0;border-radius:10px;padding:10px 14px;font:600 13px system-ui;cursor:pointer}button.secondary{background:#edf3ea;color:#244337;border:1px solid #d0ddd0}button:hover{filter:brightness(.94)}button:focus-visible,textarea:focus-visible,summary:focus-visible{outline:3px solid #749919;outline-offset:3px}textarea{display:block;width:100%;height:126px;border:1px solid #bccfc5;border-radius:10px;background:#fafcf9;padding:12px;font:13px/1.5 ui-monospace,monospace;resize:vertical;color:#15362c}label{font-weight:650;font-size:13px}details{margin-top:16px}summary{cursor:pointer;font-size:13px;font-weight:650}#status{min-height:20px;font-size:12px;color:#526f60;margin-top:8px}.error{color:#ffcfbf}.footer{font-size:12px;color:#627b72;margin-top:16px}.empty{font-size:18px;color:#c7dacd}.source-card{background:#f4f7f3;border:1px solid #dbe4d8;border-radius:10px;padding:12px;overflow-wrap:anywhere;white-space:pre-wrap}.source-list{display:flex;flex-wrap:wrap;gap:8px;max-height:170px;overflow:auto}.source-list .source-card{flex:1;min-width:100px}.code{background:#f5f8f2}mark{background:#f2ffc2;color:#183a2d;padding:2px 5px;border-radius:4px}@media(max-width:620px){main{padding:15px}.grid{grid-template-columns:1fr}.panel{padding:16px}header{align-items:flex-start}.tag{display:none}h1{font-size:25px}.cards{grid-template-columns:repeat(auto-fit,minmax(125px,1fr))}.source-list{max-height:120px}pre{max-height:150px}}</style></head><body><main>
<header><div><div class="eyebrow">JavaScript • Math log10</div><h1>Powers-of-ten explorer</h1><div class="muted">One input, one operation, one observable result.</div></div><span class="tag">Starter example</span></header>
<section class="panel"><label for="input">Input data (JSON)</label><textarea id="input" maxlength="10000" spellcheck="false"></textarea><div class="toolbar"><button id="run" type="button">Update preview</button><button class="secondary" id="original" type="button">Original data</button><button class="secondary" id="changed" type="button">Changed data</button><button class="secondary" id="edge" type="button">Empty / zero case</button></div><div id="status" role="status" aria-live="polite"></div></section>
<div class="grid"><section class="panel code"><h2>The operation</h2><pre id="expression"></pre></section><section class="panel result"><h2>Returned result</h2><pre id="result" aria-live="polite"></pre></section></div><section class="panel"><h2>Source after the operation</h2><pre id="source"></pre></section>
<p class="footer">Local sample data only. No server request, account, or installation is needed.</p></main><script>
'use strict';
const initial = "1000";
const alternate = "1001";
const empty = "0";
const input = document.getElementById('input');
const output = document.getElementById('result');
const source = document.getElementById('source');
const status = document.getElementById('status');
function transform(data) { return Math.log10(data); }
function readable(value) {
if (value === undefined) return 'undefined';
if (typeof value === 'number' && Object.is(value, -0)) return '-0';
return JSON.stringify(value, (_, v) => typeof v === 'number' && !Number.isFinite(v) ? String(v) : v, 2);
}
function renderCards(value, host) {
host.replaceChildren();
if (Array.isArray(value)) {
if (!value.length) {const p=document.createElement('p');p.className='empty';p.textContent='No items returned';host.append(p);return;}
const grid=document.createElement('div');grid.className='cards';
value.slice(0,40).forEach((item,index)=>{const card=document.createElement('div');card.className='card';const label=document.createElement('small');label.textContent='Item '+(index+1);card.append(label);appendValue(item,card);grid.append(card);});host.append(grid);
if(value.length>40){const p=document.createElement('p');p.textContent='Showing 40 of '+value.length+' items.';host.append(p);}
} else if(value && typeof value==='object'){const card=document.createElement('div');card.className='card';appendValue(value,card);host.append(card);}
else {const p=document.createElement('div');p.className='hero';p.textContent=typeof value==='boolean'?(value?'Yes · true':'No · false'):value===undefined?'No value · undefined':value===''?'Empty string':String(value);host.append(p);}
}
function appendValue(value,host){
if(value && typeof value==='object' && !Array.isArray(value))Object.entries(value).slice(0,40).forEach(([key,item])=>{const row=document.createElement('div');row.className='field';const label=document.createElement('small');label.textContent=key;const text=document.createElement('span');text.className='value';text.textContent=typeof item==='string'?item:readable(item);row.append(label,text);host.append(row);});
else {const text=document.createElement('div');text.className='value';text.textContent=typeof value==='string'?value:readable(value);host.append(text);}
}
function update(){
try{
if(input.value.length>10000)throw new Error('Keep this sample below 10,000 characters.');
const data=JSON.parse(input.value);const before=readable(data);const result=transform(data);const after=readable(data);
output.textContent=readable(result);source.textContent=after;
output.classList.remove('error');status.textContent='Preview updated. '+(before===after?'Data values unchanged.':'Source data changed in place.');
}catch(error){output.replaceChildren();output.classList.add('error');output.textContent=error.name+': '+error.message;source.replaceChildren();status.textContent='Check the JSON and the input shape. Restore Original data to start again.';}
}
document.getElementById('run').addEventListener('click',update);
[['original',initial],['changed',alternate],['edge',empty]].forEach(([id,value])=>document.getElementById(id).addEventListener('click',()=>{input.value=value;update();}));
document.getElementById('expression').textContent="Math.log10(data)";
input.value=initial;update();
</script></body></html>
A logarithm is not a digit count
The real-number domain here is positive values. Zero returns -Infinity, and negative values return NaN. A friendly explainer should reject those inputs or display a clearly labeled special case rather than putting either result into an ordinary exponent card.
Do not confuse the logarithm with a digit count. For example, log10(1000) is 3 while the decimal integer label has four digits. A digit-count formula needs its own assumptions and boundary handling.
Floating-point results near powers of ten can also require care if a later step rounds the exponent. Validate that boundary behavior before using a logarithm to assign discrete categories.
Explore values above and below one
Try 1, 10, 100, and 1000, then try 0.1. The latter should produce -1, showing that a negative exponent is valid even though a negative input is not.
For an extension, show the reconstruction 10 raised to the calculated exponent beside the source value. Use a reasonable display precision and explain that the reconstruction may be approximate for arbitrary floating-point inputs.
The MDN reference for Math.log10() documents the method's full behavior and browser compatibility.
For help editing the sample input, the JSON guide explains valid JSON and how parsing turns it into JavaScript values.
Share a working explanation
A powers-of-ten page is most useful when the reader can explore values between the familiar examples. Share the complete file through HTML to link on NOS so they can try positive values themselves. Keep the positive-input requirement visible instead of relying on a link to explain invalid cases later.