Sig Fig Calculator

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sig fig calculator
Identify Sig Figs (One Number)Addition / SubtractionMultiplication / Division
+-×÷
Answer:
function toggleInputs(){var mode=document.getElementById('operation_type').value;var r2=document.getElementById('row2');var ro=document.getElementById('row_op');var l1=document.getElementById('label1′);if(mode==='identify'){r2.style.display='none';ro.style.display='none';l1.innerHTML='Number:';}else{r2.style.display='table-row';ro.style.display='table-row';l1.innerHTML='Number 1:';}}function countSigFigs(str){str=str.trim();if(!str||isNaN(parseFloat(str)))return 0;var n=str.replace(/^-/,");if(n.indexOf('.')!==-1){var parts=n.split('.');var whole=parts[0];var frac=parts[1];if(parseFloat(whole)===0){var firstNonZero=frac.search(/[1-9]/);return firstNonZero===-1?0:frac.length-firstNonZero;}else{return whole.replace(/^0+/,").length+frac.length;}}else{return n.replace(/^0+/,").replace(/0+$/,").length;}}function getDecimalPlaces(str){str=str.trim();if(str.indexOf('.')===-1)return 0;return str.split('.')[1].length;}function roundTo(num,sigFigs){if(num===0)return 0;var d=Math.ceil(Math.log10(num<0?-num:num));var power=sigFigs-d;var magnitude=Math.pow(10,power);var shifted=Math.round(num*magnitude);return shifted/magnitude;}function calculateSigFigs(){var mode=document.getElementById('operation_type').value;var s1=document.getElementById('input1').value;var showSteps=document.getElementById('show_steps').checked;var ansDiv=document.getElementById('answer');var out="";if(mode==='identify'){var count=countSigFigs(s1);if(count===0){alert('Invalid Number');return;}out="Number: "+s1+"
Significant Figures: "+count+"";if(showSteps){out+="
Rules: Non-zero digits are always significant. Leading zeros are placeholders. Trailing zeros after a decimal point are significant.";}}else{var s2=document.getElementById('input2').value;var op=document.getElementById('op_select').value;var n1=parseFloat(s1);var n2=parseFloat(s2);if(isNaN(n1)||isNaN(n2)){alert('Please enter two valid numbers');return;}var rawResult;if(op==='+')rawResult=n1+n2;else if(op==='-')rawResult=n1-n2;else if(op==='*')rawResult=n1*n2;else rawResult=n1/n2;var finalResult;var reason="";if(mode==='add_sub'){var d1=getDecimalPlaces(s1);var d2=getDecimalPlaces(s2);var minD=Math.min(d1,d2);finalResult=rawResult.toFixed(minD);reason="Result rounded to "+minD+" decimal places (least precise input).";}else{var c1=countSigFigs(s1);var c2=countSigFigs(s2);var minC=Math.min(c1,c2);finalResult=roundTo(rawResult,minC);reason="Result rounded to "+minC+" significant figures (least precise input).";}out="Calculation: "+s1+" "+op+" "+s2+"
Raw Result: "+rawResult+"
Correct Sig Fig Result: "+finalResult+"";if(showSteps){out+="
"+reason+"";}}ansDiv.innerHTML=out;ansDiv.style.display='block';}

How to Use the Sig Fig Calculator

The sig fig calculator is an essential tool for chemistry, physics, and engineering students. Significant figures (sig figs) represent the precision of a measurement. This tool helps you identify how many digits in a number are meaningful and performs arithmetic operations while maintaining scientific accuracy.

Simply select your calculation type, enter your values, and the calculator will apply the standard rules of significant figures to provide a correctly rounded result.

Identify Mode
Enter a single number to find out how many significant figures it contains. For example, 0.0050 has two sig figs.
Addition/Subtraction
Used when adding or subtracting values. The result is rounded based on the decimal place of the least precise measurement.
Multiplication/Division
Used when multiplying or dividing. The result is rounded to the same number of sig figs as the input with the fewest sig figs.

Significant Figure Rules

When using the sig fig calculator, it follows these standard scientific rules:

  • All non-zero digits are significant: 1, 2, 3, 4, 5, 6, 7, 8, 9 always count.
  • Zeros between non-zeros: These are significant (e.g., 101 has 3 sig figs).
  • Leading zeros: These are NEVER significant; they are just placeholders (e.g., 0.002 has 1 sig fig).
  • Trailing zeros in a decimal: These are significant (e.g., 12.00 has 4 sig figs).
  • Trailing zeros in an integer: Usually not significant unless marked with a decimal (e.g., 100 has 1 sig fig, but 100. has 3).

Calculation Examples

Example 1: Multiplication

Calculate: 2.5 × 3.42

  1. 2.5 has 2 significant figures.
  2. 3.42 has 3 significant figures.
  3. Raw result = 8.55
  4. Rounding to 2 sig figs (the lower count) = 8.6

Example 2: Addition

Calculate: 10.1 + 7.452

  1. 10.1 has 1 decimal place.
  2. 7.452 has 3 decimal places.
  3. Raw result = 17.552
  4. Rounding to 1 decimal place = 17.6

Common Questions

Why do we use sig figs?

Significant figures ensure that the final result of a calculation doesn't appear more precise than the original measurements used to get it.

Are exact numbers significant?

Exact numbers (like "12 eggs" or the "2" in the formula for circumference) have an infinite number of significant figures and do not limit the precision of a calculation.

What about scientific notation?

In scientific notation (e.g., 4.50 x 10³), all digits in the coefficient (4.50) are significant. This is often the best way to avoid ambiguity with trailing zeros.

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