Determine the correct number of significant figures for your calculations.
Sig Digit Calculator
Enter a single number, a value in scientific notation, or a simple arithmetic operation (add, subtract, multiply, divide).
Significant Figures—
Input Value—
Operation Type—
Resulting Precision Rule—
Formula: Significant figures are determined by specific rules for counting digits, especially concerning leading/trailing zeros and operations.
What is Sig Digit Calculation?
Sig digit calculation, more formally known as significant figures or sig figs, is a fundamental concept in science, engineering, and mathematics that deals with the precision of numerical values. It's not just about counting digits; it's about conveying the reliability and accuracy of a measurement or a calculated result. In essence, significant figures indicate how many digits in a number are known with certainty, plus one digit that is estimated or uncertain. Mastering sig digit calculation is crucial for avoiding the propagation of uncertainty in scientific work and ensuring that results reflect the true precision of the underlying data.
Anyone working with measurements or performing calculations based on measured data needs to understand sig digit calculation. This includes students in introductory science and math courses, researchers, chemists, physicists, engineers, and even technicians in various fields. A common misconception is that all digits in a number are equally important or accurate. However, the reality is that measurements are always limited by the precision of the instrument used. For example, stating a length as "12.3 meters" implies a different level of precision than "12.30 meters." The extra zero in the latter suggests the measurement was made with an instrument capable of distinguishing to the hundredths place. Properly applying sig digit calculation ensures that calculated values don't appear more precise than the original measurements.
Sig Digit Calculation Formula and Mathematical Explanation
There isn't a single, simple algebraic formula for sig digit calculation in the way there is for, say, calculating a loan payment. Instead, it's governed by a set of rules applied to both individual numbers (measurements) and the results of arithmetic operations. The goal is to maintain the appropriate level of precision throughout a calculation.
Rules for Counting Significant Figures in a Single Number:
Non-zero digits are always significant. (e.g., 123 has 3 sig figs)
Zeros between non-zero digits are always significant. (e.g., 104.06 has 5 sig figs)
Leading zeros (zeros to the left of the first non-zero digit) are never significant. They only indicate the position of the decimal point. (e.g., 0.0052 has 2 sig figs: 5 and 2)
Trailing zeros (zeros at the end of a number) are significant IF the number contains a decimal point. (e.g., 12.00 has 4 sig figs; 50.0 has 3 sig figs)
Trailing zeros in a whole number without a decimal point are ambiguous. To avoid ambiguity, use scientific notation. (e.g., 1500 could have 2, 3, or 4 sig figs. Written as 1.5 x 103 it has 2 sig figs; 1.50 x 103 has 3; 1.500 x 103 has 4).
Rules for Significant Figures in Operations:
Multiplication and Division: The result should have the same number of significant figures as the measurement with the fewest significant figures.
Addition and Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
Rounding: If the digit to be dropped is 5 or greater, round up the last significant digit. If it's less than 5, keep the last significant digit as it is. If the digit is exactly 5 followed only by zeros, follow the "round half to even" rule (round to the nearest even digit) or the simpler "round half up" rule, depending on convention. For simplicity in many introductory contexts, "round half up" is often used.
The calculator applies these rules based on the input provided and the detected operation type to determine the correct number of significant figures.
Variable Explanations for Sig Digit Calculation Rules:
Variables in Sig Digit Rules
Variable/Concept
Meaning
Unit
Typical Range
Non-zero Digit
Any digit from 1 through 9.
N/A
1-9
Zero
The digit 0. Its significance depends on its position and context (leading, between non-zeros, trailing).
N/A
0
Decimal Point
A symbol separating the whole number part from the fractional part of a number. Crucial for determining trailing zero significance.
N/A
Present or Absent
Scientific Notation
A way of expressing numbers that are too large or too small to be conveniently written in decimal form (e.g., a x 10^b). Essential for removing ambiguity in trailing zeros.
N/A
Varies
Significant Figures (Sig Figs)
The count of digits in a number that are known with certainty, plus one estimated digit. Indicates precision.
Count (dimensionless)
1 or more
Decimal Places
The number of digits to the right of the decimal point. Key for addition/subtraction rules.
Count (dimensionless)
0 or more
Practical Examples (Real-World Use Cases)
Let's illustrate sig digit calculation with practical scenarios:
Example 1: Measuring Length
Scenario: A student measures the length of a table using a tape measure that is marked to the nearest centimeter. They find the length to be 156 centimeters. Later, they need to calculate the perimeter of the room, and another wall measures 234 centimeters.
Inputs:
Length 1: 156 cm
Length 2: 234 cm
Calculation & Sig Digits:
Individual Measurements: 156 has 3 sig figs (all non-zero). 234 has 3 sig figs (all non-zero).
Operation: If we need to add these for a perimeter calculation (e.g., Perimeter = 2 * (Length 1 + Length 2)), we first add: 156 cm + 234 cm = 390 cm.
Rule for Addition: The rule states the result should have the same number of decimal places as the measurement with the fewest decimal places. Both 156 and 234 have zero decimal places. Therefore, the sum 390 should be reported with zero decimal places.
Result: The sum is 390 cm. How many sig figs does 390 have? Since it's a whole number ending in a trailing zero without a decimal point shown, it's technically ambiguous. However, following the addition rule (maintaining the fewest decimal places, which is zero), we keep the number as 390. To be unambiguous about the precision, it might be better expressed in scientific notation if the zero is significant: 3.90 x 102 cm (3 sig figs). If the zero is not significant, it would be 3.9 x 102 cm (2 sig figs). Based on the initial measurements, the precision is to the nearest whole centimeter, so 390 cm is the correct result, implying 3 sig figs if the zero is considered significant due to context or a convention of not dropping trailing zeros in addition/subtraction results unless explicitly required. In this case, 390 implies the value is precise to the tens place. Let's assume standard rounding rules, 156 + 234 = 390. The result has 3 significant figures.
Financial Interpretation: In inventory management or cost estimation based on lengths, reporting 390 cm is more accurate than, say, 390.0 cm (implying precision to the nearest tenth) or 39 cm (losing too much precision). Accurate inventory valuation relies on precise measurements.
Example 2: Chemical Concentration Calculation
Scenario: A chemist titrates an acid solution. They measure 25.50 mL of acid using a burette (4 sig figs) and find it reacts completely with 18.2 mL of a base solution. They need to calculate the concentration of the base.
Inputs:
Volume of Acid: 25.50 mL
Volume of Base: 18.2 mL
Calculation & Sig Digits:
Individual Measurements: 25.50 mL has 4 sig figs. 18.2 mL has 3 sig figs.
Operation: Concentration is often calculated by Volume of Acid / Volume of Base (or moles, but let's simplify). Calculation: 25.50 mL / 18.2 mL.
Rule for Division: The result must have the same number of significant figures as the number with the fewest significant figures. Here, 18.2 mL has 3 sig figs, which is the minimum.
Calculation Result: 25.50 / 18.2 = 1.4010989…
Rounding: Rounding to 3 significant figures gives 1.40.
Result: The calculated concentration value should be reported as 1.40 (with units, e.g., Molarity). This maintains the precision dictated by the least precise measurement (the volume of the base).
Financial Interpretation: In pharmaceutical manufacturing or chemical sales, the precise concentration of a product directly impacts its efficacy and value. Reporting 1.40 M instead of 1.4010989 M avoids overstating the product's quality and ensures compliance with regulatory standards. Understanding cost per unit calculation is vital here.
How to Use This Sig Digit Calculator
Using our Sig Digit Calculator is straightforward and designed to provide instant clarity on the number of significant figures for various inputs.
Enter Your Value or Calculation: In the "Enter Number or Calculation" field, type the number you want to analyze. This can be a simple number (like 123.45), a number in scientific notation (like 1.5e4 or 1.5 x 10^4), or a basic arithmetic expression involving two numbers (like 5.6 + 7.89, 100 / 25, 12 * 3.4, or 99 – 10.5).
Click "Calculate Sig Digits": Once your input is entered, click the "Calculate Sig Digits" button.
Review the Results:
Main Result: The largest display shows the total number of significant figures determined for your input.
Intermediate Values: Below the main result, you'll see the original input value, the type of operation detected (if any), and the specific rule applied (e.g., "Multiplication/Division Rule", "Addition/Subtraction Rule", "Non-zero Digit Rule").
Formula Explanation: A brief textual explanation reinforces the core concept of sig fig determination.
Understand the Precision: The number of sig figs directly relates to the precision of the data. More sig figs generally mean higher precision.
Decision Making: Use the calculated sig figs to report your results accurately in scientific reports, lab work, or any situation where measurement precision matters. For instance, when performing multiple calculations, carry extra digits through intermediate steps and only round the final answer to the correct number of sig figs, as guided by the rules. Financial forecasting often requires careful handling of precision.
Copy Results: If you need to document your findings, use the "Copy Results" button to copy the main result, intermediate values, and the rule applied.
Reset: Click "Reset" to clear the fields and start a new calculation.
Key Factors That Affect Sig Digit Results
Several factors influence how significant figures are determined and reported, extending beyond simple counting rules:
Precision of Measurement Instruments: This is the most fundamental factor. A high-precision instrument (like a digital scale measuring to 0.001g) yields numbers with more significant figures than a low-precision one (like a balance scale measuring to 0.1g). The sig figs of a measurement directly reflect the instrument's capability. Asset valuation requires understanding the precision of appraisal tools.
The Nature of the Operation (Add/Subtract vs. Multiply/Divide): As detailed in the rules, addition and subtraction are limited by decimal places (place value), while multiplication and division are limited by the count of significant figures. This difference arises from how errors propagate in different mathematical operations.
Ambiguity of Trailing Zeros: Whole numbers ending in zeros are inherently ambiguous regarding their significant figures (e.g., 200 could have 1, 2, or 3 sig figs). Using scientific notation (e.g., 2.0 x 102 vs. 2.00 x 102) is the clearest way to eliminate this ambiguity and communicate the intended precision.
Defined Constants vs. Measured Values: Some numbers used in calculations are exact definitions or counts (e.g., the number of items in a dozen, pi to a certain number of digits if specified as exact). These numbers have an infinite number of significant figures and do not limit the precision of a calculation. Only measured values impose limits.
Rounding Conventions: While the calculator applies standard rounding, the specific convention used (e.g., "round half up," "round half to even") can slightly alter results, particularly when the digit to be dropped is exactly 5. Different scientific fields might adhere to specific rounding standards.
Significant Figures in Intermediate Calculations: To maintain accuracy, it's often advised to carry at least one or two extra digits through intermediate steps of a multi-step calculation. Only round the final result to the correct number of significant figures dictated by the least precise measurement involved in the overall calculation. Over-rounding intermediate steps can lead to substantial errors in the final answer. This is critical for complex financial modeling.
Context of the Problem: Sometimes, the context dictates interpretation. For instance, if a problem states "a speed of 50 mph," without further clarification, it's often treated as having 1 or 2 significant figures. However, if it's part of a calculation where other values have high precision, you might infer more precision is intended, or use scientific notation if explicitly defined. Risk assessment often involves interpreting data with varying implied precision.
Frequently Asked Questions (FAQ)
Q1: What's the difference between significant figures and decimal places?
Significant figures indicate the overall precision of a number, including non-zero digits and significant zeros. Decimal places refer only to the digits *after* the decimal point. The rules for addition/subtraction depend on decimal places, while multiplication/division depend on the total count of significant figures.
Q2: How do I know if trailing zeros are significant?
Trailing zeros are significant ONLY if the number contains a decimal point. For example, 120. has 3 sig figs, while 120 has an ambiguous number (likely 2). Using scientific notation (like 1.20 x 10^2 for 3 sig figs) removes ambiguity.
Q3: Does the calculator handle complex equations?
This calculator is designed for single numbers or simple binary operations (one operation at a time). For complex equations with multiple steps, you need to apply the rules sequentially, paying attention to intermediate rounding and the least precise value at each step.
Q4: What if my input is negative?
The negative sign does not affect the number of significant figures. You determine the sig figs based on the absolute value of the number. For example, -12.34 has 4 significant figures.
Q5: What about exact numbers like '2' in '2x'?
Exact numbers, such as those from definitions (e.g., 1 meter = 100 centimeters) or counting discrete items (e.g., 5 apples), have an infinite number of significant figures. They do not limit the precision of a calculation and will not affect the sig fig count of the result.
Q6: How should I report results for addition/subtraction involving numbers with different decimal places?
Identify the number with the fewest decimal places. Your final answer should be rounded to that same number of decimal places. For example, 10.1 + 5.23 = 15.33. Since 10.1 has only one decimal place, the result should be rounded to 15.3.
Q7: Can I use this for percentages?
Yes, treat percentages like any other number. For example, 25.5% has 3 significant figures. If you calculate a percentage increase, apply the rules for division/multiplication. A 10% increase on $100 ($100 * 1.10) would result in $110. Since 10% has 2 sig figs (or potentially infinite if meant exactly), and $100 has ambiguity, the result $110 is typically reported as having 2 or 3 sig figs depending on context.
Q8: Why are significant figures important in finance?
While less rigorously applied than in hard sciences, significant figures matter in finance for maintaining appropriate precision in reporting financial data, avoiding misleading accuracy, and ensuring consistency in calculations involving potentially measured economic indicators or derived financial ratios. It speaks to the quality of financial planning.
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function isValidNumber(str) {
if (str === null || str.trim() === "") return false;
// Allow numbers, scientific notation (e.g., 1.2e-3, 5E4), and simple decimals
// This regex is simplified for common cases and might not cover all edge cases of IEEE 754.
return /^-?\d+(\.\d+)?([eE][+-]?\d+)?$/.test(str);
}
function getSigFigs(numStr) {
// Handle scientific notation first
var scientificMatch = numStr.match(/^-?(\d+(\.\d+)?)[eE][+-]?(\d+)$/);
if (scientificMatch) {
numStr = scientificMatch[1]; // Use the mantissa part
}
numStr = numStr.replace(/^-/, "); // Remove negative sign for counting
// Rule 1 & 2: Non-zero digits and zeros between non-zeros are significant
var significantDigits = numStr.replace(/^[0]+/, ").replace(/[0]+$/, "); // Remove leading and trailing zeros for initial count
if (significantDigits.length === 0) { // Handle cases like 0, 0.0, 000
if (numStr.includes('.')) return 1; // 0.0 has 1 sig fig (the 0 after decimal)
return 1; // 0 has 1 sig fig by convention for calculation purposes
}
var hasDecimal = numStr.includes('.');
var numZeros = 0;
for (var i = 0; i < numStr.length; i++) {
if (numStr[i] === '0') {
numZeros++;
}
}
// Rule 3: Leading zeros are never significant
var count = numStr.replace(/^[0.]+/, '').length; // Remove leading zeros and decimal point
// Rule 4: Trailing zeros are significant if there's a decimal point
if (hasDecimal) {
count = numStr.length – numStr.replace(/[^0.]/g, '').length + (numStr.match(/\./g) ? numStr.length – numStr.replace(/[0-9]/g, '').length : 0) ; // Count digits and zeros after decimal
// A more robust way: count all digits that are not leading zeros.
// If decimal exists, ALL digits and trailing zeros are significant
var firstNonZeroIndex = -1;
for(var i = 0; i 0) { // e.g. 12.00
count = numStr.length – numStr.indexOf(numStr.replace(/^0+/, ").charAt(0));
} else if (hasDecimal) {
count = numStr.replace(/^0+/, ").length; // Simplification: count all digits after leading zeros if decimal exists
}
} else { // No decimal point
// Rule 5: Trailing zeros in whole numbers are ambiguous. Assume they are NOT significant unless part of scientific notation that clarifies.
// For simplicity in this calculator, we will count non-zero digits and zeros between them.
// Trailing zeros in whole numbers are tricky. The calculator will attempt to infer based on common usage.
// If we parse "1500", and it's not scientific notation, it's often assumed to have 2 sig figs.
// Let's count non-zero digits and zeros between them.
var digits = numStr.replace(/^0+/, ").replace(/0+$/, "); // Remove leading/trailing zeros
count = digits.length;
// Add back zeros that were BETWEEN non-zero digits if they existed
for(var i = 0; i 0 && numStr[i-1] !== '.' && i < numStr.length – 1 && numStr[i+1] !== '.'){
// Check if it's between non-zeros or preceded by non-zero and followed by non-zero or end of number after decimal
if( (numStr[i-1] !== '0' && numStr[i-1] !== '.') || (hasDecimal && i < numStr.length -1) ) {
// This logic is complex. Let's simplify: Count all digits that are not leading zeros.
// For trailing zeros without a decimal, assume they are placeholders.
count = numStr.replace(/^[0]+/, '').replace(/[0]+$/, '').length; // Count significant digits
// Check for internal zeros
for(var j=0; j 0 && numStr[j-1] !== '.' && (j 0 && numStr[numStr.length – 1] === '0' && !hasDecimal) {
// Trailing zero in whole number, ambiguous. Default to non-significant unless it's the only digit.
// Let's refine: Count digits, and zeros ONLY if they are between non-zero digits.
count = 0;
for(var k=0; k 0 && k 0 && numStr[numStr.length -1] === '0') {
// Trailing zero in whole number, default to not significant.
// This is the hardest rule to implement perfectly without context.
// The calculator's backend will try to infer based on input patterns.
// For "1500", let's assume 2 sig figs (1, 5).
// For "150", assume 2 sig figs (1, 5).
// For "50", assume 1 sig fig (5).
var trailingZeros = 0;
for(var l=numStr.length – 1; l>=0; l–){
if(numStr[l] === '0') trailingZeros++;
else break;
}
count = numStr.length – trailingZeros; // Count digits before trailing zeros
if(count === 0 && numStr.includes('0')) count = 1; // e.g. "0"
}
}
}
}
}
}
// Final pass for clarity:
var sigCount = 0;
var hasDecimalPoint = numStr.includes('.');
var digitFound = false;
for(var i = 0; i = '1' && char 0 && numStr.endsWith('0')) {
var tempStr = numStr.replace(/^0+/, "); // Remove leading zeros
var trailingZerosCount = 0;
for(var k = tempStr.length – 1; k >= 0; k–){
if(tempStr[k] === '0') trailingZerosCount++;
else break;
}
// Subtract trailing zeros unless they are the only digits (e.g., "0")
if (tempStr.length > trailingZerosCount) {
sigCount -= trailingZerosCount;
} else if (tempStr.length === trailingZerosCount && tempStr.length > 0){ // e.g., "100" -> tempStr "100", trailing 2, sig=1. "50" -> temp "50", trailing 1, sig=1
// This is still tricky. The calculator's logic is simplified.
}
}
return sigCount === 0 ? (numStr.includes('0') ? 1 : 0) : sigCount;
}
function getOperationType(input) {
if (input.includes('+') && !input.includes('-') && !input.includes('*') && !input.includes('/')) return 'Addition';
if (input.includes('-') && input.indexOf('-') > 0 && !input.includes('+') && !input.includes('*') && !input.includes('/')) return 'Subtraction'; // Ensure it's not a negative number sign
if (input.includes('*') && !input.includes('+') && !input.includes('-') && !input.includes('/')) return 'Multiplication';
if (input.includes('/') && !input.includes('+') && !input.includes('-') && !input.includes('*')) return 'Division';
// Handle combined operations or negative numbers gracefully
if (input.includes('+') || input.includes('-') || input.includes('*') || input.includes('/')) {
// Very basic detection for common operations.
if (input.includes('*') || input.includes('/')) return 'Multiplication/Division';
if (input.includes('+') || (input.includes('-') && input.indexOf('-') > 0)) return 'Addition/Subtraction';
}
return 'Single Value';
}
function getRuleApplied(operationType, values) {
if (operationType === 'Single Value') {
return "Non-zero digits, captive zeros, and trailing zeros (with decimal) are significant.";
} else if (operationType === 'Multiplication' || operationType === 'Division' || operationType === 'Multiplication/Division') {
return "Result sig figs = fewest sig figs of inputs.";
} else if (operationType === 'Addition' || operationType === 'Subtraction' || operationType === 'Addition/Subtraction') {
return "Result decimal places = fewest decimal places of inputs.";
}
return "N/A";
}
function countDecimalPlaces(numStr) {
var decimalPart = numStr.split('.')[1];
return decimalPart ? decimalPart.length : 0;
}
function calculateSigDigits() {
var inputVal = document.getElementById("numberInput").value.trim();
var mainResultElement = document.getElementById("mainResult");
var intermediateValueElement = document.getElementById("intermediateValue");
var intermediateOperationElement = document.getElementById("intermediateOperation");
var intermediateRuleElement = document.getElementById("intermediateRule");
var resultsDiv = document.getElementById("result");
var intermediateResultsDiv = document.getElementById("intermediateResults");
var explanationDiv = document.querySelector(".calculation-explanation");
var errorElement = document.getElementById("numberInputError");
// Clear previous errors
errorElement.style.display = 'none';
errorElement.textContent = ";
if (inputVal === "") {
errorElement.textContent = "Please enter a number or calculation.";
errorElement.style.display = 'block';
resultsDiv.style.display = 'none';
intermediateResultsDiv.style.display = 'none';
explanationDiv.style.display = 'none';
return;
}
var originalInputForDisplay = inputVal; // Keep original for display
// Detect operation type and values
var operationType = 'Single Value';
var values = [];
var calculatedResult = null;
var resultDecimalPlaces = Infinity;
var minSigFigs = Infinity;
var ops = ['+', '-', '*', '/'];
var detectedOp = null;
var opIndex = -1;
// Try to find the primary operation
for (var i = 0; i -1) {
// Simple logic: take the first operator found. More complex parsing needed for order of operations.
// For this calculator, we focus on simple binary ops.
if (detectedOp === null || tempOpIndex 1) {
// Reconstruct if a negative number was split
var potentialParts = [];
var currentPart = "";
for(var i = 0; i 0 && !inputVal.substring(i-1).match(/[eE]/)){ // Found a subtraction operator
potentialParts.push(currentPart.trim());
currentPart = "-"; // Start new part with the negative sign
} else {
currentPart += inputVal[i];
}
}
potentialParts.push(currentPart.trim());
parts = potentialParts.filter(p => p !== ""); // Filter out empty strings
}
if (parts.length === 2) {
var val1Str = parts[0].trim();
var val2Str = parts[1].trim();
if (!isValidNumber(val1Str) || !isValidNumber(val2Str)) {
errorElement.textContent = "Invalid number format in calculation.";
errorElement.style.display = 'block';
resultsDiv.style.display = 'none';
intermediateResultsDiv.style.display = 'none';
explanationDiv.style.display = 'none';
return;
}
values.push(val1Str);
values.push(val2Str);
var num1 = parseFloat(val1Str);
var num2 = parseFloat(val2Str);
var sig1 = getSigFigs(val1Str);
var sig2 = getSigFigs(val2Str);
var dec1 = countDecimalPlaces(val1Str);
var dec2 = countDecimalPlaces(val2Str);
minSigFigs = Math.min(sig1, sig2);
resultDecimalPlaces = Math.min(dec1, dec2);
if (detectedOp === '+') {
calculatedResult = num1 + num2;
} else if (detectedOp === '-') {
calculatedResult = num1 – num2;
} else if (detectedOp === '*') {
calculatedResult = num1 * num2;
} else if (detectedOp === '/') {
calculatedResult = num1 / num2;
}
} else {
// If split doesn't result in 2 parts, maybe it's a complex expression or invalid.
// Fallback to single value analysis.
operationType = 'Single Value';
}
}
var finalSigFigs = 0;
var finalResultStr = ";
if (operationType === 'Single Value') {
if (!isValidNumber(inputVal)) {
// Check if it's scientific notation like 1.2e4
var scientificMatch = inputVal.match(/^([\d\.]+)[eE]([+-]?\d+)$/);
if(scientificMatch) {
var mantissa = scientificMatch[1];
if(!isValidNumber(mantissa)) {
errorElement.textContent = "Invalid number format.";
errorElement.style.display = 'block';
resultsDiv.style.display = 'none';
intermediateResultsDiv.style.display = 'none';
explanationDiv.style.display = 'none';
return;
}
finalSigFigs = getSigFigs(mantissa);
finalResultStr = inputVal; // Keep original scientific notation
intermediateValueElement.textContent = inputVal;
intermediateOperationElement.textContent = "Scientific Notation";
intermediateRuleElement.textContent = "Count digits in mantissa.";
} else {
errorElement.textContent = "Invalid number format. Please enter a valid number, scientific notation, or simple calculation.";
errorElement.style.display = 'block';
resultsDiv.style.display = 'none';
intermediateResultsDiv.style.display = 'none';
explanationDiv.style.display = 'none';
return;
}
} else {
finalSigFigs = getSigFigs(inputVal);
finalResultStr = inputVal; // Use the input value itself
intermediateValueElement.textContent = inputVal;
intermediateOperationElement.textContent = "Single Measurement";
intermediateRuleElement.textContent = "Apply standard rules.";
}
} else if (calculatedResult !== null) {
var finalDecimalPlaces = countDecimalPlaces(calculatedResult.toString());
var tempResultStr = calculatedResult.toString();
if (operationType === 'Addition/Subtraction' || operationType === 'Addition' || operationType === 'Subtraction') {
// Round based on decimal places
var roundedResult = calculatedResult.toFixed(resultDecimalPlaces);
finalResultStr = roundedResult;
finalSigFigs = getSigFigs(roundedResult);
intermediateRuleElement.textContent = "Fewest decimal places (" + resultDecimalPlaces + ")";
} else { // Multiplication/Division
// Round based on minimum significant figures
finalSigFigs = minSigFigs;
// Round the calculated result to the determined significant figures
var roundedResult = parseFloat(calculatedResult.toPrecision(minSigFigs));
finalResultStr = roundedResult.toString();
intermediateRuleElement.textContent = "Fewest sig figs (" + minSigFigs + ")";
}
intermediateValueElement.textContent = values.join(" " + detectedOp + " ");
intermediateOperationElement.textContent = operationType;
// Update results div with calculation details
if (isNaN(calculatedResult)) {
errorElement.textContent = "Calculation resulted in an invalid number (e.g., division by zero).";
errorElement.style.display = 'block';
resultsDiv.style.display = 'none';
intermediateResultsDiv.style.display = 'none';
explanationDiv.style.display = 'none';
return;
}
} else {
errorElement.textContent = "Could not determine calculation type or values.";
errorElement.style.display = 'block';
resultsDiv.style.display = 'none';
intermediateResultsDiv.style.display = 'none';
explanationDiv.style.display = 'none';
return;
}
mainResultElement.textContent = finalSigFigs;
resultsDiv.style.display = 'block';
intermediateResultsDiv.style.display = 'block';
explanationDiv.style.display = 'block';
// Update chart data
updateChart(finalSigFigs, intermediateValueElement.textContent, operationType);
}
function resetCalculator() {
document.getElementById("numberInput").value = "";
document.getElementById("mainResult").textContent = "–";
document.getElementById("intermediateValue").textContent = "–";
document.getElementById("intermediateOperation").textContent = "–";
document.getElementById("intermediateRule").textContent = "–";
document.getElementById("result").style.display = 'none';
document.getElementById("intermediateResults").style.display = 'none';
document.getElementById("numberInputError").style.display = 'none';
document.getElementById("numberInputError").textContent = ";
document.querySelector(".calculation-explanation").style.display = 'none';
clearChart();
}
function copyResults() {
var mainResult = document.getElementById("mainResult").textContent;
var intermediateValue = document.getElementById("intermediateValue").textContent;
var intermediateOperation = document.getElementById("intermediateOperation").textContent;
var intermediateRule = document.getElementById("intermediateRule").textContent;
var inputVal = document.getElementById("numberInput").value;
if (mainResult === "–") return; // Nothing to copy
var textToCopy = "Sig Digit Calculation Results:\n\n";
textToCopy += "Input Value/Calculation: " + inputVal + "\n";
textToCopy += "Determined Operation: " + intermediateOperation + "\n";
textToCopy += "Rule Applied: " + intermediateRule + "\n";
textToCopy += "\n";
textToCopy += "— Final Result —\n";
textToCopy += "Number of Significant Figures: " + mainResult + "\n";
textToCopy += "Resulting Value (if calculated): " + intermediateValue + "\n";
// Use navigator.clipboard for modern browsers
if (navigator.clipboard && navigator.clipboard.writeText) {
navigator.clipboard.writeText(textToCopy).then(function() {
alert("Results copied to clipboard!");
}).catch(function(err) {
console.error('Async: Could not copy text: ', err);
fallbackCopyTextToClipboard(textToCopy);
});
} else {
fallbackCopyTextToClipboard(textToCopy);
}
}
function fallbackCopyTextToClipboard(text) {
var textArea = document.createElement("textarea");
textArea.value = text;
// Avoid scrolling to bottom
textArea.style.top = "0";
textArea.style.left = "0";
textArea.style.position = "fixed";
document.body.appendChild(textArea);
textArea.focus();
textArea.select();
try {
var successful = document.execCommand('copy');
var msg = successful ? 'Results copied to clipboard!' : 'Failed to copy results.';
alert(msg);
} catch (err) {
console.error('Fallback: Oops, unable to copy', err);
alert('Failed to copy results.');
}
document.body.removeChild(textArea);
}
// Charting Logic
var chartInstance = null;
var chartCanvas = document.getElementById("sigDigitChart");
if (chartCanvas) {
var ctx = chartCanvas.getContext('2d');
chartInstance = new Chart(ctx, {
type: 'bar', // Changed to bar for better comparison
data: {
labels: ['Input Sig Figs', 'Result Sig Figs'],
datasets: [{
label: 'Significant Figures',
data: [0, 0], // Placeholder
backgroundColor: [
'rgba(0, 74, 153, 0.6)', // Primary color
'rgba(40, 167, 69, 0.6)' // Success color
],
borderColor: [
'rgba(0, 74, 153, 1)',
'rgba(40, 167, 69, 1)'
],
borderWidth: 1
}]
},
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
y: {
beginAtZero: true,
title: {
display: true,
text: 'Number of Significant Figures'
}
}
},
plugins: {
title: {
display: true,
text: 'Comparison of Input and Result Significant Figures'
},
legend: {
display: false // Hide legend as labels are clear
}
}
}
});
} else {
console.error("Canvas element not found for chart.");
}
function updateChart(resultSigFigs, inputValue, operationType) {
if (!chartInstance) return;
var inputSigFigs = 0;
if (operationType === 'Single Value') {
// Try to parse the inputValue as a number or scientific notation
var cleanedInput = inputValue.replace(/,/g, "); // Remove commas
if (cleanedInput.includes('e') || cleanedInput.includes('E')) {
var mantissa = cleanedInput.split(/[eE]/)[0];
inputSigFigs = getSigFigs(mantissa);
} else {
inputSigFigs = getSigFigs(cleanedInput);
}
} else {
// For operations, we need to get sig figs of individual components
var parts = inputValue.split(/[\+\-\*\/]/); // Basic split
if(parts.length === 2) {
var val1 = parts[0].trim();
var val2 = parts[1].trim();
var sig1 = getSigFigs(val1);
var sig2 = getSigFigs(val2);
// In operations, the input sig figs is determined by the MINIMUM sig figs of the operands
inputSigFigs = Math.min(sig1, sig2);
} else {
// Fallback if parsing fails, use the result sig figs for input sig figs too
inputSigFigs = resultSigFigs;
}
}
// Ensure inputSigFigs is a valid number, default to 0 if not calculable
if (isNaN(inputSigFigs) || inputSigFigs < 0) inputSigFigs = 0;
if (isNaN(resultSigFigs) || resultSigFigs < 0) resultSigFigs = 0;
chartInstance.data.datasets[0].data = [inputSigFigs, resultSigFigs];
chartInstance.update();
}
function clearChart() {
if (chartInstance) {
chartInstance.data.datasets[0].data = [0, 0];
chartInstance.update();
}
}
// Initial calculation on load if there's a default value (optional)
// calculateSigDigits();