SIGNIFICANT FIGURES RULES

GENERAL RULES[1]

1. All non-zero digits are significant.
• Example:  123.7 has 4 significant figures

1. All zeros between non-zero digits are significant.
• Example:  1207 has 4 sig. figs., 120.007 has 6 sig. Figs.

1. All zeros at the left of the number are NOT significant.
• Example:  0.00032 has 2 sig. figs, 0.03 has 1 sig. Fig.

When zeros are at the right of the number:

1. If there is no decimal, the zeros are NOT significant.
• Example:  300 has 1 sig. fig., 25400 has 3 sig. Figs.

1. If there is a decimal, the zeros ARE significant.
• Example:  60.0 has 3 sig. figs., 0.00045300 has 5 sig. figs.  (the 4 zeros at the left of the number do not count, but the 2 zeros at the right of the number do count).

MULTIPLYING/DIVIDING:

Round to the number of significant figures as the number that has the fewest numbers

Examples:          4.00   x    3  =     12      →       10

3 s.f.    1 s.f.      2 s.f.  round to 1 s.f.

60.0    ÷     20.0   =  3         →    3.00

3 s.f.              3 s.f.     1 s.f.  round to 3 s.f.

Round to the PLACE that is the least precise coming in.  (choose the place of the last SIGNIFICANT digit)

Examples:      40.56  (hundredths place)

9.4        (tenths place)← least precise

+        117.321   (thousandths place)

167.281  round to 167.3 (tenths place)

110   (tens place)

-        65.4  (tenths place)

44.6 round to 40 (tens place)

[1] “Stoichiometry Tutorials.” Significant Figures. Accessed 25 Oct. 2018.