Significant Figures

Significant figures (sig figs) are the meaningful digits in a number that contribute to its precision. They are used in science and engineering to communicate how accurately a value has been measured.

Rules for Counting Significant Figures

Rule	Example	Sig Figs
All non-zero digits are significant	4,782	4
Zeros between non-zero digits are significant	5,008	4
Trailing zeros after a decimal point are significant	3.500	4
Leading zeros (before the first non-zero digit) are NOT significant	0.0042	2
Trailing zeros in a whole number (ambiguous without decimal point)	3,600 (ambiguous)	2, 3 or 4

Rounding to Significant Figures

Count from the first non-zero digit to the required number of sig figs.
Look at the next digit: if 5–9, round up; if 0–4, round down.
Replace all subsequent digits with zeros (whole numbers) or drop them (decimals).

Worked Examples

Number	Round to	Result
73,462	3 sig figs	73,500
0.004826	2 sig figs	0.0048
9.9975	4 sig figs	10.00
150,800	3 sig figs	151,000

Why Significant Figures Matter

Suppose you measure a room as 5 m wide and a tile as 0.3 m. Dividing: 5 ÷ 0.3 = 16.666... – but your measurement was only accurate to 1 sig fig, so the answer should be stated as 17, not 16.666.

Significant figures ensure that a calculated answer does not claim more accuracy than the original measurements justify.

Key Points

Non-zero digits are always significant.
Zeros between non-zeros are always significant.
Leading zeros are never significant.
Trailing zeros after the decimal point are significant.
When rounding, do not claim more sig figs than your least precise measurement.

Practice: Count the Significant Figures

A number is shown below. If you get the count wrong (or leave it blank), we'll apply the rules together.

How many significant figures does this number have?

Summary

Significant figures express the precision of a measurement. By carefully counting and rounding to the correct number of sig figs, scientists and engineers avoid overstating the accuracy of their results. Mastering sig figs is essential for chemistry, physics, engineering, and any data-driven field.