Notes 3 Significant Figures
Reference Sheet
Name_____________________________________
Date___________ Block_____
Rules for identification of significant figures (a.k.a. sig. figs. or s.f.)
1. All NONZERO numbers are significant.
2. A zero that is the terminal number (LAST number) AFTER a decimal is significant.
3. Any zeros that are BETWEEN significant numbers are significant.
4. Zeros that act as placeholders are NOT significant.
Examples: (the sig. figs. have been underlined)
146.9 m has 4 s.f. (all the numbers are nonzero)
146.0 m has 4 s.f. (the 1, 4, and 6 are nonzero, and the zero is the last number AFTER the
decimal)
1460 m has 3 s.f. (the 1, 4, and 6 are significant; the zero is a place holder)
1408 m has 4 s.f. (the 1, 4, and 8 are nonzero; the zero is inbetween significant numbers)
15 000 000 m has only 2 s.f. (the 1 and the 5 are nonzero; the zeros are placeholders)
0.000 100 km has 3 s.f. (the 1 is nonzero; the terminal zero is significant so the zero between
the 1 and the terminal zero is also significant; the zero before the decimal is not significant; the
zeros after the decimal but before the 1 are acting as placeholders and are not significant)
Underline the significant numbers in each of the following measurements:
0.25 g
250 g
2 500 m
250.0 mL
148.005 cm
0.000 04 km
0.000 040 km
2050 cg
400 m
0.100 006 mm
0.001 010 cm
5.4030 x 108 m
Rules for calculations with significant figures.
Addition and Subtraction
1. Look at the measurements you are using in the calculation. Identify the measurement that
has the LEAST number of decimal places. Your final answer cannot have more
decimal places or fewer decimal places than that measurement.
2. Add or subtract as usual. Then ROUND YOUR ANSWER TO THE APPROPRIATE
NUMBER OF DECIMAL PLACES.
9.0 m
9.1 m
+9 m
27.1 m = 27 m

18.005 L
9.1
L
8.905 L = 8.9 L
The addition answer is rounded to 27 m with no decimal places because 9 m has no decimal
place.
The subtraction answer is rounded to 8.9 L because 9.1 L has only 1 decimal place.
Multiplication and Division
1. Look at the measurements you are using in the calculation. Identify the measurement
having the LEAST number of significant figures. Your final answer cannot have
more sig. figs. or fewer sig. figs. than that measurement.
2. Multiply or divide as usual. Then ROUND YOUR ANSWER TO THE APPROPRIATE
NUMBER OF SIGNIFICANT FIGURES.
21.5 m
x 2.5 m
54.25 m2 = 54 m2
300.45 m2 
5 m = 60.09 m = 60 m
The multiplication answer is rounded to 54 m2 because 2.5 m has only 2 sig. figs.
The division answer is rounded to 60 m because 5 m has only 1 sig. fig.
REMEMBER: WHEN ROUNDING YOUR ANSWERS, DO
THE PLACE VALUE OF ANY NUMBER!!!!!
NOT CHANGE