Sig Fig Calculator
Category: Number & Notation ToolsCalculate significant figures and perform calculations with proper sig fig rules
Explanation
Rules for Counting Significant Figures
Rule 1: Non-Zero Digits
All non-zero digits are significant.
Example: 123 has 3 significant figures.
Rule 2: Zeros Between Non-Zero Digits
Zeros between non-zero digits are significant.
Example: 1002 has 4 significant figures.
Rule 3: Leading Zeros
Leading zeros (zeros to the left of the first non-zero digit) are not significant.
Example: 0.0123 has 3 significant figures.
Rule 4: Trailing Zeros in Decimal Numbers
Trailing zeros (zeros at the end of a number) that come after a decimal point are significant.
Example: 12.300 has 5 significant figures.
Rule 5: Trailing Zeros in Integers
Trailing zeros in a whole number (without a decimal point) may or may not be significant. Without additional context, they are ambiguous.
Example: 1200 has 2, 3, or 4 significant figures, depending on the precision of measurement.
To indicate that trailing zeros are significant, use scientific notation or include a decimal point:
- 1.200 × 10³ or 1200. (4 significant figures)
- 1.20 × 10³ (3 significant figures)
- 1.2 × 10³ (2 significant figures)
Rules for Calculations with Significant Figures
Addition and Subtraction
For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places.
Example: 12.52 + 5.7 = 18.2
5.7 has 1 decimal place, so the answer has 1 decimal place.
Multiplication and Division
For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures.
Example: 4.5 × 2.31 = 10
4.5 has 2 significant figures, so the answer has 2 significant figures.
Exact Numbers
If one of the numbers in a calculation is exact (like a defined quantity), it doesn't limit the number of significant figures in the result.
Example: Converting 5.70 meters to centimeters: 5.70 m × 100 = 570 cm
100 is exact, so the answer has 3 significant figures (from 5.70).
Rounding
When rounding to the correct number of significant figures:
- If the next digit is less than 5, round down.
- If the next digit is greater than 5, round up.
- If the next digit is exactly 5, round to the nearest even digit.
Significant Figures Examples
Counting Significant Figures
| Number | Significant Figures | Explanation |
|---|---|---|
| 123 | 3 | All non-zero digits are significant |
| 1.23 | 3 | The decimal point doesn't affect significance |
| 0.123 | 3 | Leading zeros are not significant |
| 1.230 | 4 | Trailing zeros after a decimal point are significant |
| 1200 | 2-4* | Ambiguous: 1.2×10³ (2), 1.20×10³ (3), or 1.200×10³ (4) |
| 1200. | 4 | Decimal point indicates all zeros are significant |
| 0.0120 | 3 | Leading zeros not significant, trailing zero is significant |
*Ambiguous without additional notation.
Calculations with Significant Figures
Addition: 12.52 + 5.7 = 18.2 (not 18.22)
Subtraction: 15.7 - 2.315 = 13.4 (not 13.385)
Multiplication: 3.14 × 2.1 = 6.6 (not 6.594)
Division: 8.75 ÷ 4.1 = 2.1 (not 2.134)
Count It Right, Every Time
Ever been stuck wondering how many digits actually matter in a number like 0.00450 or 1200? That’s where the Sig Fig Calculator steps in to help. This handy tool figures out the significant figures in any number you type. These are the digits that tell you how precise a number is.
Let’s say you’re doing science homework or double-checking a measurement. You want your answer to be accurate, but not more detailed than your numbers allow. That’s the whole point of significant figures! They keep math honest.
Using this calculator can help save time, cut down on mistakes, and make your answers more exact. No need to count digits by hand or wonder if that zero at the end really matters.
What Makes This Calculator Tick?
The Sig Fig Calculator does two main things:
- Counts Significant Figures
- Enter any number (like 0.00340 or 25,000).
- It tells you how many digits matter and why.
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Gives a breakdown explaining the count.
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Does Math with Sig Figs
- Choose an operation: +, –, ×, or ÷.
- Enter two numbers.
- It gives you the right answer, rounded to the correct number of significant figures.
- Explains how it got there.
Helping Out with Real-Life Stuff
This calculator isn’t just for science class. You can use it in everyday moments, too:
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Schoolwork:
If you're solving chemistry problems, this helps make sure your answer isn't too short or too long. -
Money math:
When you're rounding prices or working with decimals, the calculator keeps things accurate. -
Quick checks:
Maybe you're curious about a weird number you saw—like 0.0005400—and want to know what’s actually meaningful.
Here’s a quick example:
You’re multiplying 4.5 × 2.31.
The calculator tells you the answer is 10 because 4.5 has only 2 significant figures. So the answer should also have 2.
How To Use It Like a Pro
Whether you're just starting out or already comfortable with sig figs, here’s how to use the calculator:
To Count Sig Figs:
- Click the "Count Sig Figs" tab.
- Type your number in the box.
- Press "Count Significant Figures."
- Read the answer and check out the explanation.
To Do Math with Sig Figs:
- Click the "Sig Fig Calculations" tab.
- Type the first number.
- Choose your operation (Add, Subtract, Multiply, or Divide).
- Type the second number.
- Press "Calculate with Sig Figs."
- See your answer and learn how it was rounded.
Need to try again? Just hit Reset and go again.
Crunching the Final Numbers
The Sig Fig Calculator takes the guesswork out of tricky numbers. Whether you're adding measurements in lab class or double-checking a number for a report, this tool keeps your answers clear and correct.
And yes—we’ve tested this in a competitive digital world full of other tools. While some options might delve too deep or say goodbye to simplicity, this one keeps things easy.
The next time you see a number like 0.00780 and wonder what counts, you’ll know what to do. Just plug it into the Sig Fig Calculator—and let the math do the talking.