1. Counting Significant Figures:
1) All non-zero digits are significant.
1.5 has 2 significant figures.
2) Interior (sandwich) zeros (between two digits) are significant.
1.05 has 3 significant figures.
3) Trailing zeros after a decimal point are significant.
1.050 has 4 significant figures.
Tro's "Introductory Chemistry", Chapter 2

2. Counting Significant Figures, Continued
4) Leading zeros (on the left of a number) are NOT significant.
has 4 significant figures.
5) Zeros that do nothing but set the decimal point (to the right of a number) are NOT significant:
So 150 has 2 significant figures.
542,000, has 3 significant figures.
Tro's "Introductory Chemistry", Chapter 2

3. Tro's "Introductory Chemistry", Chapter 2
Practice:
How many significant figures are in each of the following numbers? a) b) c)
d) 2.97 ×
e) 100,000---
2 sig. fig.
(leading zeros are not significant).(Rule #4).
4 sig. fig.
(zeros after the decimal & interior zeros are significant). (Rules #2 & 3).
4 sig. fig.
(all non zeros digits are significant).(Rule #1).
3 sig. fig.
(all non zeros digits are significant)
(Rule #1).
1 sig. fig.
(zeros to the right of a # with out decimal point are not significant) (Rule #5).
Tro's "Introductory Chemistry", Chapter 2

4. Rules for rounding numbers:
If the digit immediate right of the last significant
figure is:
a) greater than 5 – Round up the last sig. figure:
2.54
b) lesser than 5 – Do NOT round up:
2.53
c) equal to 5:

5. c) equal to 5:
1) followed by a non-zero –ROUND UP:
2.54
2) followed by zero:
If the last significant figure:
- is an odd digit – ROUND UP:
- is an even digit– Do NOT round up:
2.52

6. Tro's "Introductory Chemistry", Chapter 2
Rounding to 2 significant figures:
2.34 rounds to:
2.3
2.37 rounds to:
2.4
rounds to:
rounds to:
or × 10-2
rounds to:
or × 10-2
Tro's "Introductory Chemistry", Chapter 2

7. Rounding Rules in Addition & Subtraction:
The result must be rounded up to the same number of digits after the decimal point than the measurement with the fewest number of digits after the decimal point: cm cm cm
cm ≈

8. Rounding Rules in Addition & Subtraction:
The result must be rounded up to the same number of digits after the decimal point than the measurement with the fewest number of digits after the decimal point: cm cm cm
cm ≈
77.2 cm

9. Tro's "Introductory Chemistry", Chapter 2
Practice:
1) =
2) =
9.214
= 9.21
2 decimal
places
3 decimal
places
3 decimal
places
0.835
= 0.8
1 decimal
place
3 decimal
places
Tro's "Introductory Chemistry", Chapter 2

10. Rounding Rules in Multiplication & Division:
The answer must have the same number of significant figures as the measurement with the fewest number of significant figures:
24 x 3.28 =
23.5 x 1.2 =
60.2 ÷ 20.1 =
78.72
≈ 79
28.2
≈ 28
2.995
≈ 3.00

11. Tro's "Introductory Chemistry", Chapter 2
Practice:
1) 5.02 × × 0.10 = 2) ÷ 6.10 = 3) 1.01 × 0.12 × ÷ 96 = 4) × ÷ =
= 45
3 sig. figs.
5 sig. figs.
2 sig. figs.
= 0.966
4 sig. figs.
3 sig. figs.
= 0.068
3 sig. figs.
4 sig. figs.
2 sig. figs.
2 sig. figs.
= 1.52
4 sig. figs.
3 sig. figs.
6 sig. figs.
Tro's "Introductory Chemistry", Chapter 2