3.2Significant Figures: The 5 Rules

Decimal places count from the point, so they cannot compare $528.3$ cm with $5.3$ m fairly. Significant figures count from the first non-zero digit, which measures precision itself.

Shaded digits count. A trailing zero in a whole number is dashed because it is ambiguous on its own.

The five rules, in one table

Read down the table rather than memorising five separate rules; the only question is whether a zero counts.

The digits	Significant?	Example
Non-zero digits	always	$4849$ has 4 s.f.
Zeros between non-zero digits	yes	$6.0705$ has 5 s.f.
Zeros before the first non-zero digit	no, they are placeholders	$0.0083$ has 2 s.f.
Zeros after a non-zero digit, in a decimal	yes, they show precision	$24.60$ has 4 s.f.
Zeros at the end of a whole number	ambiguous on their own	$3600$ may be 2, 3 or 4 s.f.

For that last row, the number of significant figures depends on the accuracy the value was measured or rounded to, so a question will tell you.

Counting significant figures

State the number of significant figures in: (a) $\displaystyle 0.02070$ (b) $\displaystyle 50\,004$ (c) $\displaystyle 8.00$

Show solution▾

(a) Leading zeros (

0.0

) are not significant (Rule 3). The zero between 2 and 7 is significant (Rule 2). Trailing zero is significant (Rule 4). Digits: 2, 0, 7, 0. Answer: 4 s.f.

(b) Zeros between 5 and 4 are significant (Rule 2). Digits: 5, 0, 0, 0, 4. Answer: 5 s.f.

Now you try

State the number of significant figures in $827$ .

Show solution▾

All non-zero digits are significant (Rule 1).

827

has

3

significant figures.

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Now you try

State the number of significant figures in $0.00073$ .

Show solution▾

Leading zeros are not significant (Rule 3). Digits: 7, 3.

0.00073

has

2

significant figures.

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