Significant Figures in Multiplication and Division
The answer must have the same number of sig figs as the input with the fewest — no more, no less. Here is how it works.
Reviewed by the Sig Figs Calc Editorial Team · Last updated April 2025 · See methodology
The rule for multiplication and division
The answer must have the same number of significant figures as the input with the fewest significant figures.
For example: 4.560 × 2.1 = 9.6
The raw product is 9.576. But 2.1 has only 2 sig figs — so the answer is limited to 2 sig figs: 9.6.
The logic behind this: the precision of a product or quotient cannot exceed the precision of the least precise measurement used to calculate it.
Why the fewest sig figs controls the answer
Significant figures represent measurement precision. When you multiply two measured values, the result inherits the uncertainty of the least precise measurement. It would be misleading to report more precision in the answer than your instruments actually provided.
Think of it this way: if you measure a room as 4.5 m × 3.214 m, you only know the first dimension to 2 sig figs. Reporting the area as 14.463 m² implies a precision you do not have. The correct answer is 14 m².
This is different from addition and subtraction
Addition and subtraction use fewest decimal places — not sig fig count. See the addition and subtraction guide →
How to apply the rule — step by step
Count the sig figs in each operand
Apply the sig fig rules to every number in the expression. Record the count for each.
Identify the limiting value
The input with the fewest sig figs is the limiting value. Your answer cannot be more precise than this.
Perform the multiplication or division
Calculate the full raw answer using all digits. Do not round the operands first.
Round the answer to match the limiting sig fig count
Round the raw result so it has the same number of sig figs as the limiting value. Use standard rounding: if the next digit is ≥ 5, round up.
Check for trailing zero ambiguity
If your answer is a whole number ending in zeros, consider using scientific notation to make the sig fig count unambiguous.
Worked examples
Four examples — from basic to scientific notation.
4.560 × 2.1
2.1 has the fewest sig figs (2). The raw product 9.576 rounds to 9.6.
8.40 ÷ 2.0
2.0 has 2 sig figs. The quotient 4.2 already has 2 sig figs — no further rounding needed.
1.23 × 4.567 × 0.01
0.01 has only 1 sig fig. The raw product rounds to 0.06 (1 sig fig).
6.02 × 10²³ × 1.5
1.5 limits to 2 sig figs. 9.03 × 10²³ rounds to 9.0 × 10²³.
Mixed operations
When an expression combines multiplication/division with addition/subtraction, evaluate each operation in sequence. Apply the correct rule — fewest sig figs for × ÷, fewest decimal places for + − — at each step. Carry intermediate results with full precision and only round at the final step.
Example
2.4 × 3.65 + 1.2
Step 1: 2.4 × 3.65 → 2 sf (limited by 2.4) → intermediate: 8.76 (carry full precision)
Step 2: 8.76 + 1.2 → 1 dp (limited by 1.2) → 10.0
Common errors
✗ Using decimal places instead of sig figs
For multiplication and division, you count total sig figs — not decimal places. Decimal places are the rule for addition and subtraction. These are two separate rules for two separate operations.
✗ Rounding operands before calculating
Always compute the full raw answer first, then round once at the end. Rounding each operand introduces compounding errors that can significantly change the result.
✗ Not identifying the limiting operand correctly
The limiting operand is the one with the fewest sig figs — not the smallest number or the one with fewest digits. 0.01 has 1 sig fig, even though 100 looks like a "bigger" number.
✗ Forgetting to check trailing zero ambiguity in the answer
If rounding gives you a whole number like 400, it is unclear how many sig figs it has. Use scientific notation (4 × 10² or 4.0 × 10²) to show the correct count explicitly.
Frequently asked questions
Common questions about sig figs in multiplication and division.
More significant figures guides
Explore rules, examples, and operation guides.
Sig Figs Calculator
Solve any expression with step-by-step sig figs output.
Addition & Subtraction
A different rule: fewest decimal places — not sig figs.
Significant Figures Rules
All 7 rules that govern significant figures.
Rounding to Sig Figs
Step-by-step rounding guide with worked examples.
Scientific Notation
Multiplication in scientific notation — with sig figs.
Examples Hub
Multiplication and division examples by category.