.significant-figure-calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
max-width: 700px;
margin: 20px auto;
padding: 25px;
border: 1px solid #e0e0e0;
border-radius: 10px;
background-color: #f9f9f9;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
}
.significant-figure-calculator-container h2 {
color: #333;
text-align: center;
margin-bottom: 25px;
font-size: 28px;
}
.significant-figure-calculator-container .input-group {
margin-bottom: 18px;
display: flex;
flex-direction: column;
}
.significant-figure-calculator-container label {
margin-bottom: 8px;
color: #555;
font-weight: bold;
font-size: 16px;
}
.significant-figure-calculator-container input[type="number"],
.significant-figure-calculator-container input[type="text"] {
width: calc(100% – 20px);
padding: 12px;
border: 1px solid #ccc;
border-radius: 6px;
font-size: 16px;
box-sizing: border-box;
transition: border-color 0.3s ease;
}
.significant-figure-calculator-container input[type="number"]:focus,
.significant-figure-calculator-container input[type="text"]:focus {
border-color: #007bff;
outline: none;
}
.significant-figure-calculator-container button {
background-color: #007bff;
color: white;
padding: 14px 25px;
border: none;
border-radius: 6px;
cursor: pointer;
font-size: 18px;
font-weight: bold;
width: 100%;
transition: background-color 0.3s ease, transform 0.2s ease;
margin-top: 20px;
}
.significant-figure-calculator-container button:hover {
background-color: #0056b3;
transform: translateY(-2px);
}
.significant-figure-calculator-container .result-container {
margin-top: 30px;
padding: 20px;
border: 1px solid #d4edda;
background-color: #e9f7ef;
border-radius: 8px;
text-align: center;
font-size: 18px;
color: #155724;
font-weight: bold;
}
.significant-figure-calculator-container .result-container strong {
color: #0a3622;
}
.significant-figure-calculator-container .error-message {
color: #dc3545;
margin-top: 10px;
text-align: center;
font-weight: bold;
}
.significant-figure-calculator-container p {
line-height: 1.6;
color: #444;
margin-bottom: 15px;
}
.significant-figure-calculator-container h3 {
color: #333;
margin-top: 30px;
margin-bottom: 15px;
font-size: 22px;
}
.significant-figure-calculator-container ul {
list-style-type: disc;
margin-left: 20px;
margin-bottom: 15px;
color: #444;
}
.significant-figure-calculator-container ul li {
margin-bottom: 8px;
}
Significant Figure Calculator
Rounded Number:
function calculateSignificantFigures() {
var originalNumberInput = document.getElementById("originalNumber").value;
var sigFigsInput = document.getElementById("sigFigs").value;
var resultContainer = document.getElementById("resultContainer");
var roundedNumberDisplay = document.getElementById("roundedNumber");
var errorMessageDisplay = document.getElementById("errorMessage");
errorMessageDisplay.textContent = "";
resultContainer.style.display = "none";
var num = parseFloat(originalNumberInput);
var sigFigs = parseInt(sigFigsInput, 10);
if (isNaN(num)) {
errorMessageDisplay.textContent = "Please enter a valid number for 'Original Number'.";
return;
}
if (isNaN(sigFigs) || sigFigs <= 0 || !Number.isInteger(sigFigs)) {
errorMessageDisplay.textContent = "Please enter a positive integer for 'Desired Significant Figures'.";
return;
}
if (num === 0) {
roundedNumberDisplay.textContent = "0";
resultContainer.style.display = "block";
return;
}
var isNegative = num < 0;
var absNum = Math.abs(num);
// Determine the exponent (power of 10) of the most significant digit
var exponent = Math.floor(Math.log10(absNum));
// Calculate the scaling factor
// This factor shifts the most significant digit to the 'sigFigs' position before rounding
var factor = Math.pow(10, sigFigs – 1 – exponent);
// Multiply by factor, round, then divide by factor
var rounded = Math.round(absNum * factor) / factor;
// Reapply the sign
var finalResult = isNegative ? -rounded : rounded;
// Special handling for displaying trailing zeros if necessary to meet sig figs,
// especially for numbers like 120 (2 sig figs) vs 120.0 (4 sig figs).
// The numerical value is correct, but string representation might need adjustment.
// For simplicity and common use, we'll display the numerical result.
// If a specific string format is needed (e.g., "120.0" for 4 sig figs from 120.00),
// more complex string manipulation would be required, which is beyond basic numerical rounding.
// The current method provides the numerically correct value rounded to sig figs.
roundedNumberDisplay.textContent = finalResult.toString();
resultContainer.style.display = "block";
}
Understanding Significant Figures
Significant figures (often called "sig figs" or "s.f.") are the digits in a number that carry meaning contributing to its precision. They are crucial in scientific and engineering fields to express the accuracy of measurements and calculations. When you perform calculations with measured values, the result should not imply greater precision than the least precise measurement used.
Rules for Identifying Significant Figures
- Non-zero digits: All non-zero digits are significant. (e.g., 123.45 has 5 sig figs)
- Zeros between non-zero digits: Zeros located between non-zero digits are significant. (e.g., 2005 has 4 sig figs)
- Leading zeros: Zeros that come before all non-zero digits (leading zeros) are NOT significant. They only indicate the position of the decimal point. (e.g., 0.0012 has 2 sig figs)
- Trailing zeros (with decimal point): Trailing zeros (at the end of the number) are significant if the number contains a decimal point. (e.g., 12.00 has 4 sig figs, 120. has 3 sig figs)
- Trailing zeros (without decimal point): Trailing zeros in a whole number without a decimal point are generally ambiguous. To clarify, scientific notation is often used. (e.g., 1200 could have 2, 3, or 4 sig figs. 1.2 x 103 has 2 sig figs, 1.20 x 103 has 3 sig figs). Our calculator will treat these as non-significant unless a decimal is present.
Rounding to Significant Figures
Rounding a number to a specific number of significant figures involves identifying the significant digits and then adjusting the number based on the digit immediately following the last significant digit.
- If the digit to be dropped is 5 or greater, round up the last retained digit.
- If the digit to be dropped is less than 5, keep the last retained digit as it is.
- When rounding whole numbers, replace dropped digits with zeros to maintain the number's magnitude.
Examples of Rounding
- 123.456 to 3 significant figures: The first three significant figures are 1, 2, 3. The next digit is 4 (less than 5), so we round down. Result: 123.
- 0.007892 to 2 significant figures: The leading zeros are not significant. The first two significant figures are 7, 8. The next digit is 9 (5 or greater), so we round up the 8. Result: 0.0079.
- 56789 to 4 significant figures: The first four significant figures are 5, 6, 7, 8. The next digit is 9 (5 or greater), so we round up the 8. We replace the dropped digit with a zero to maintain magnitude. Result: 56790.
- 1.995 to 3 significant figures: The first three significant figures are 1, 9, 9. The next digit is 5, so we round up the last 9. This causes a cascade. Result: 2.00. (Note: The trailing zeros are significant here).
How to Use This Calculator
Simply enter the number you wish to round into the "Original Number" field. Then, specify the desired number of significant figures in the "Desired Significant Figures" field. Click "Calculate" to see the rounded result. This tool is perfect for students, scientists, and engineers who need to quickly and accurately round numbers to the correct precision.