Significant Figures Calculator (Step-by-Step)

Count sig figs instantly and perform combined operations (+, −, ×, ÷) with rules applied automatically. Unlike other calculators, we show you why at every step.

📖 How to Use This Calculator

Type your expression in the text box using the keyboard (e.g., 12.5 * 3.2)

Click "Solve" or press Enter to calculate

View results: exact result, rounded result (with correct sig figs), and scientific notation

Expand "Step by Step" to see how sig figs were identified and which rules were applied

Optional: Select a specific number of sig figs (1-5) to round your result differently

Copy & Share: Use buttons to copy results or share the calculation link

💡 Pro Tip: Use * for multiply, / for divide, ^ for exponents, and 3e2 for scientific notation (3×10²).

Video Tutorial: Master Significant Figures

Prefer watching? Here's the best explanation by The Organic Chemistry Tutor.

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How to Identify Significant Figures

Mastering significant figure rules is essential in chemistry and physics. Our calculator applies these rules automatically, but understanding them helps you verify your results.

The 5 Golden Rules of Significant Figures

Non-zero digits are ALWAYS significant

Example: 1234 has 4 sig figs, 56.78 has 4 sig figs

Zeros BETWEEN non-zero digits are significant

Example: 101 has 3 sig figs, 5.007 has 4 sig figs

Leading zeros are NEVER significant

Example: 0.005 has 1 sig fig, 0.0420 has 3 sig figs

Trailing zeros AFTER the decimal point ARE significant

Example: 2.50 has 3 sig figs, 3.0 has 2 sig figs

Trailing zeros WITHOUT a decimal point are AMBIGUOUS

Example: 100 could have 1, 2, or 3 sig figs — use scientific notation to be clear!

Tricky Examples That Often Confuse Students

These are the numbers that confuse students the most. Use our calculator to verify your answers and study these examples to avoid common mistakes in your chemistry homework.

Number	Sig Figs	Explanation
100	1	Trailing zeros without a decimal point are NOT significant. Classic trap!
1000	1	Same rule: trailing zeros without decimal don't count. Write 1000. to indicate 4 sig figs.
100.	3	The decimal point makes ALL digits significant, including the zeros.
3.0	2	The zero after the decimal point IS significant. The .0 matters!
2.0	2	Same rule: 2.0 has 2 sig figs because trailing zeros after decimal count.
5.0	2	The zero after the decimal indicates measurement precision, so it's significant.
0.005020	4	Leading zeros don't count (0.00), but trailing zeros after decimal do (5020).
1.00 × 10³	3	Scientific notation removes ambiguity. The coefficient clearly shows 3 sig figs.

Operations with Significant Figures

The rules for calculating significant figures differ between multiplication/division and addition/subtraction. Our calculator handles both automatically and shows which rule applies at each step.

× ÷ Multiplication & Division Rule

The result must have the same number of significant figures as the value with the fewest sig figs.

2.0 × 3.15 = ?

2.0 has 2 sig figs, 3.15 has 3 sig figs

Calculator shows: 6.3

Answer: 6.3 (2 sig figs)

+ − Addition & Subtraction Rule

The result must have the same number of decimal places as the value with the fewest decimal places.

12.52 + 1.3 = ?

12.52 has 2 decimal places, 1.3 has 1 decimal place

Calculator shows: 13.82

Answer: 13.8 (1 decimal place)

Mixed Operations (PEMDAS)

For expressions with multiple operations, follow order of operations (PEMDAS). Keep all digits in intermediate steps and round only the final result. Our calculator does this automatically — try 12.5 * 3.2 + 1.5 to see it in action!

How to Round Significant Figures

After calculating, you need to round correctly. Rounding rules in chemistry are straightforward, and our calculator applies them automatically.

Standard

If the digit to drop is 5 or greater, round up

Example: 2.35 → 2.4 (rounding to 2 sig figs)

Standard

If the digit to drop is less than 5, round down

Example: 2.34 → 2.3 (rounding to 2 sig figs)

Advanced

Banker's Rounding (round to nearest even)

When the digit is exactly 5, round to the nearest even number. Used in advanced contexts, but most chemistry classes use standard rounding.

Scientific Notation and Significant Figures

Scientific notation eliminates ambiguity in significant figures. When you're unsure how many sig figs a number like "300" has, scientific notation makes it perfectly clear.

300

Ambiguous (1, 2, or 3 sig figs?)

3.0 × 10²

Clear: 2 sig figs

3.00 × 10²

Clear: 3 sig figs

Tip: Enter scientific notation using E notation: type 3e2 for 3 × 10² or 5.5e-3 for 5.5 × 10⁻³.

Frequently Asked Questions

How many significant figures does 100 have?

100 has only 1 significant figure. The trailing zeros are NOT significant because there's no decimal point. This is one of the most common mistakes! To indicate 3 sig figs, write "100." with a decimal point, or use scientific notation: 1.00 × 10².

How many significant figures does 1000 have?

1000 has 1 significant figure by default. The three zeros are just placeholders, not measured values. To indicate more precision, use: 1000. (4 sig figs), 1.0 × 10³ (2 sig figs), or 1.000 × 10³ (4 sig figs).

How many significant figures does 3.0 have?

3.0 has 2 significant figures. The zero after the decimal point IS significant because it indicates the measurement was precise to the tenths place. This is different from writing just "3", which has 1 sig fig.

Do exact numbers have significant figures?

Exact numbers (like counting 12 eggs, or defined values like 1 inch = 2.54 cm exactly) have infinite significant figures. They don't limit the precision of your calculation because they're not measured values.

Do leading zeros ever count as significant?

No, leading zeros NEVER count as significant figures. They're just placeholders to indicate the position of the decimal point. For example, 0.005 has only 1 sig fig (the 5). The zeros before it just indicate magnitude.

Why do we need significant figures?

Significant figures communicate the precision of a measurement. When you measure something as 2.5 cm, you're saying it's between 2.45 and 2.55 cm. Reporting a result as 2.5000000 cm would falsely imply more precision than you actually have.

How do I use this calculator?

Simply type your expression in the text box (e.g., 12.5 * 3.2) and click 'Solve'. The calculator will show the exact result, the rounded result with correct sig figs, and a step-by-step explanation. You can use +, -, *, / for operations and parentheses for grouping.

Why does my answer appear in scientific notation?

When a number has trailing zeros that would be ambiguous (like 40 with 2 sig figs), we display it in scientific notation (4e+1) to clearly indicate the precision. This is the scientifically correct way to express such numbers.

Can I enter scientific notation?

Yes! Use E notation: type 3e2 for 3×10², or 5.5e-3 for 5.5×10⁻³. This is especially useful when you need to specify exact sig figs in numbers like 300 (ambiguous) vs 3.00e2 (3 sig figs).

What operations does this calculator support?

Our calculator supports addition (+), subtraction (-), multiplication (*), division (/), exponents (^), parentheses for grouping, and functions like log() and ln(). It automatically applies the correct sig fig rules for each type of operation.

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