Analyze number properties, count significant digits, and convert to scientific notation.
Significant Figures:–
Scientific Notation:–
Engineering Notation:–
Rounded Value:–
Number Type:–
Understanding Calculator Numbers and Significant Figures
In mathematics and science, not all "calculator numbers" are created equal. Significant figures (often called sig figs) represent the precision of a measurement. When you enter numbers into a calculator, it is vital to understand which digits actually contribute to the accuracy of your results.
The Rules of Significant Figures
Non-zero digits: All digits from 1 to 9 are always significant.
Zeros between digits: Zeros trapped between non-zero numbers (e.g., 101) are significant.
Leading zeros: Zeros at the beginning of a decimal (e.g., 0.005) are NOT significant; they are just placeholders.
Trailing zeros: In a number with a decimal point, trailing zeros (e.g., 45.00) are significant. In a whole number like 500, they are generally considered ambiguous unless marked.
Real-World Example:
If a scale measures a chemical at 0.00450 grams:
The first three zeros are placeholders.
The 4 and 5 are significant.
The final zero is significant because it indicates the precision of the scale.
Total Sig Figs: 3
Scientific vs. Engineering Notation
Scientific notation represents numbers as a coefficient between 1 and 10 multiplied by a power of 10. Engineering notation is similar but restricts the exponent to a multiple of three (3, 6, 9, etc.), which aligns with standard metric prefixes like kilo, mega, and micro.
function analyzeNumber() {
var rawInput = document.getElementById('numberInput').value.trim();
var roundRequest = document.getElementById('roundTo').value;
var resultsBox = document.getElementById('results');
if (rawInput === "" || isNaN(parseFloat(rawInput))) {
alert("Please enter a valid numeric value.");
return;
}
var num = parseFloat(rawInput);
var sigFigs = countSignificantFigures(rawInput);
// 1. Significant Figures Count
document.getElementById('sigFigCount').innerText = sigFigs;
// 2. Scientific Notation
document.getElementById('scientificNotation').innerText = num.toExponential();
// 3. Engineering Notation
document.getElementById('engineeringNotation').innerText = toEngineering(num);
// 4. Number Type
var typeStr = "Integer";
if (rawInput.indexOf('.') !== -1) {
typeStr = "Decimal / Float";
}
document.getElementById('numType').innerText = typeStr;
// 5. Rounding Logic
if (roundRequest && roundRequest > 0) {
document.getElementById('roundedRow').style.display = 'flex';
document.getElementById('roundedValue').innerText = roundToSigFigs(num, parseInt(roundRequest));
} else {
document.getElementById('roundedRow').style.display = 'none';
}
resultsBox.style.display = 'block';
}
function countSignificantFigures(n) {
var str = n.toString().replace(/^-/, "); // Remove negative sign
if (str.indexOf('.') !== -1) {
// Handle Decimals
var parts = str.split('.');
var before = parts[0];
var after = parts[1];
if (parseInt(before) === 0) {
// Case 0.00123 -> leading zeros not significant
var match = after.match(/[1-9]/);
if (match) {
return after.substring(match.index).length;
}
return 0;
} else {
// Case 12.340 -> everything significant
return before.length + after.length;
}
} else {
// Handle Whole Numbers (Integers)
// Note: Trailing zeros in integers are technically ambiguous,
// but standard convention often treats them as non-significant.
var matchNonZero = str.match(/[1-9]/g);
if (!matchNonZero) return 0;
// Strip leading zeros
str = str.replace(/^0+/, ");
// Standard convention: strip trailing zeros for integers
return str.replace(/0+$/, ").length;
}
}
function toEngineering(num) {
if (num === 0) return "0";
var exp = Math.floor(Math.log10(Math.abs(num)));
var engExp = Math.floor(exp / 3) * 3;
var pre = num / Math.pow(10, engExp);
return pre.toFixed(3) + " x 10^" + engExp;
}
function roundToSigFigs(num, n) {
if (num === 0) return 0;
var d = Math.ceil(Math.log10(num < 0 ? -num : num));
var power = n – d;
var magnitude = Math.pow(10, power);
var shifted = Math.round(num * magnitude);
return shifted / magnitude;
}