Physics

Significant figures

Tap a digit to see why it counts.

Significant figures

Non-zero digit. Every non-zero digit is significant.Zero between digits. A zero between two non-zero digits is significant.Leading zero. Leading zeros only fix the decimal point, so they are not significant.Trailing zero after the point. Trailing zeros in a number with a decimal point are significant.Trailing zero, no point. Trailing zeros in a number without a decimal point are not counted. Write 1.00 × 10² to make them count.Digit of a in a × 10ⁿ. In a × 10ⁿ every digit of a is significant, including its zeros. Counted and defined numbers, such as 3 coins or 100 cm in a metre, are exact and have unlimited significant figures.

Type a number

Tap a digit to see why it counts.

2significant figures

Scientific notation2.5 × 10⁻³

Round to

2

significant figures

0.00250.0025

Nothing is dropped.

Try

Add, subtract, multiply, divide

Add or subtract. The answer keeps as many decimal places as the number that has the fewest. Multiply or divide. The answer keeps as many significant figures as the number that has the fewest. The rounding is done once, on the exact result.

4.2374 significant figures
2.513 significant figures

Exact result1.68804780876

Multiply or divide: keep the fewest significant figures.

Reported1.693 significant figures

Worked examples

How many significant figures in

Rounding

Round a number

Same chapter

Error analysis Unit converter Dimensional formula

Questions students ask

Counting and rounding

What are significant figures?

They are the digits of a measured number that carry meaning: all the certain digits and the first uncertain one. The more significant figures, the more precise the measurement.

How do I count significant figures?

Every non-zero digit counts. Zeros between non-zero digits count. Zeros at the start never count. Trailing zeros count only when the number has a decimal point. So 0.0025 has 2, 500 has 1 and 500.0 has 4.

Do the zeros in 100 count?

Without a decimal point the trailing zeros are not counted, so 100 has 1 significant figure. This is open to doubt, so write 1.00 × 10² for 3 or 1 × 10² for 1.

How do I round to a number of significant figures?

Keep the first digits and look at the first one dropped. If it is more than 5 the last kept digit goes up by one, and if it is less than 5 it stays. If it is exactly 5, the last kept digit stays when it is even and goes up when it is odd, so 2.745 and 2.735 both give 2.74.

How many significant figures does the answer of a calculation have?

For addition and subtraction the answer keeps as many decimal places as the number with the fewest. For multiplication and division it keeps as many significant figures as the number with the fewest. 4.237 divided by 2.51 is 1.69.

Does changing units change the number of significant figures?

No. 4.700 m, 470.0 cm and 4.700 × 10³ mm all have 4 significant figures. Use scientific notation, rather than adding or removing zeros, when you change units.