This slideshow presents the rules of significant figures and explains how to express the answers to mathematical operations in the correct number of significant figures.

1. Significant Figures
(sig figs)

2. 28 mL
28.3 mL
28.32 mL

4. 2.55
2.5

5. 1. All non-zero digits are significant.
2. Zeros that are sandwiched between non-zero digits are significant.
3. Preceding zeros are NEVER significant.
4. Trailing zeros are not significant if there is NO decimal point.
5. Trailing zeros are significant if there is decimal point.
6. In scientific notation, all digits before the ✕ are significant.
The Rules of Significant Figures

6. 1. All non-zero digits are significant.
234
14
53498
2742
3 significant figures
4 sig figs
2 sig figs
5 sig figs

7. 2. Zeros that are sandwiched between non-zero
digits are significant.
26047
1401
202
12.07
5 significant figures
4 sig figs
4 sig figs
3 sig figs

8. 3. Preceding zeros are NEVER significant.
0.023
0.000102
0.01008
0.000007
2 significant figures
1 sig figs
3 sig figs
4 sig figs

9. 4. Trailing zeros are not significant if there is
NO decimal point.
23470
230
202000
126000
4 significant figures
3 sig figs
2 sig figs
3 sig figs

10. 5. Trailing zeros are significant if there is decimal point.
23.470
0.00230
202.000
126000.
5 significant figures
6 sig figs
3 sig figs
6 sig figs

11. 6. In scientific notation, all digits before the ✕ are significant.
6.09020 ✕ 104
6.02 ✕ 1023
2.000 ✕ 104
2.3000 ✕ 10-8
6 significant figures
5 sig figs
3 sig figs
4 sig figs

12. 0.00085
8001
7.00
700
700.
83.90
0.085600
8900000000
8900.00000
6.2300 ✕ 10-4
→ 2 sig figs
→ 4 sig figs
→ 3 sig figs
→ 1 sig fig
→ 3 sig figs
→ 4 sig figs
→ 5 sig figs
→ 2 sig figs
→ 9 sig figs
→ 5 sig figs

13. Division and multiplication:
1. Count the number of sig figs in the numbers that you multiply or divide.
2. Note which number has the least number of sig figs.
3. Make calculations and write the answer.
4. The answer cannot contain more sig figs than the number being multiplied or divided
with the least number of sig figs.
148 ÷ 12 = 12.333
800
133.50 ÷ 0.00506 = 26383.4
96 x 8 = 768
177.8 x 15 = 1667
Calculator will show you this but these
answers have too many sig figs.
26400
12
1700

14. 4. The answer cannot contain more sig figs than the number being multiplied or divided
with the least number of sig figs.
148 ÷ 12 = 12.333 = 12
96 x 8 = 768 = 800
1 sig fig
2 sig figs The answer must have only 1 sig fig
2 sig figs
3 sig figs
The answer must
have 2 sig figs

15. 4. The answer cannot contain more sig figs than the number being multiplied or divided
with the least number of sig figs.
133.50 ÷ 0.00506 = 26383.4 = 26400
177.8 x 15 = 1667 = 1700 The answer must have 2 sig figs
2 sig figs
The answer must
have 3 sig figs
4 sig figs
3 sig figs5 sig figs

16. Addition and subtraction:
1. Count the numbers of decimal places to determine the number of sig figs.
2. Note which number has the least number places after the decimal point.
3. Make calculations and write the answer.
4. The answer cannot contain more places after the decimal point than the smallest
number of decimal places in the numbers being added or subtracted.
264.6 + 78.43 = 343.03
2.8450 + 0.1 = 2.9450
356.946 - 4.7 = 352.246
Your calculator will show you this, however these
numbers have too many places after decimal point!
343.0
2.9
352.2

17. 4. The answer cannot contain more places after the decimal point than the smallest
number of decimal places in the numbers being added or subtracted.
264.6 + 78.43 = 343.03 = 343.0
2.8450 + 0.1 = 2.9450 = 2.9
1 number after
decimal place
2 numbers after decimal place
The answer must
have 1 number after
decimal place
4 numbers after
decimal place
1 number after
decimal place
The answer must have 1
number after decimal place

18. 4. The answer cannot contain more places after the decimal point than the smallest
number of decimal places in the numbers being added or subtracted.
356.946 - 4.76 = 352.186 = 352.19
9.9 + 0.7667 = 10.6667 = 10.7
2 numbers after
decimal place
The answer must have 2
numbers after decimal place
3 numbers after
decimal place
1 number after
decimal place
4 numbers after
decimal place
The answer must have 1
number after decimal place

19. - the way that scientists easily handle very large numbers or
very small numbers.
0.00006310 6.310 x 10-5
12 g of carbon contains:
6.02 x 1023 atoms602000000000000000000000 atoms

20. 0.00006310 6.310 x 10-5
1200 1.2 x 103
6310000000 6.31 x 109
60200. 6.0200 x 104
6678000000 6.678 x 109