1. Chemistry Notes Significant Figures & Scientific Notation

2. Describing Numbers
We can describe and use numbers in several different ways. These include scientific notation and significant figures.

3. Scientific Notation
In scientific notation, a number is written as the product of two numbers: a coefficient and 10 raised to a power.

4. Examples: Convert to or from Scientific Notation: 2.41 x 102 241 =
662
.0034
241 =
6015 = = =
6.62 x 102 =
3.4 x 10-3 =

5. Significant Figures
Significant figures are the numbers in a measurement that “matter”.

6. Rules for determining Significant Figures 1
Rules for determining Significant Figures 1. All non-zero digits are significant.
1, 2, 3, 4, 5, 6, 7, 8, 9

7. 2. Zeros between non-zero digits are significant
2. Zeros between non-zero digits are significant. (AKA captive or trapped zeros)
102
7002
3 sig figs
4 sig figs

8. 3. Leading zeros (zeros at the beginning of a measurement) are NEVER significant.
00542
0.0152
3 sig figs
3 sig figs

9. 4. Trailing zeros (zeros after last integer) are significant only if the number contains a decimal point.
210.0 4
5240 3 3
0.860
5240. 4 3
5240.0 5
524000

11. 5. All digits in the coefficient are significant in scientific notation.
2.1 x 10-5
6.02 x 1023 2 3

12. 6. Exact numbers have unlimited Significant Figures
Examples:
1 dozen = exactly 12

13. Examples: How many significant digits do each of the following numbers contain:
a) d) b) e) c) f) x 1023 2 2 2 5 3 4

14. Rounding:  5 round up < 5 round down (don’t change) Examples:
Round to 1 significant digit =
Round to 3 sig. digs. =
Round to 2 =
Round 65,002 to 2 sig. digs. = 40
61.6
0.016
65,000 or 6.5 x104

15. Addition and Subtraction
– The measurement with the fewest decimal places to the right of the decimal point determines the number of decimal places in the answer.

16. Examples: Solve using correct significant figures 45.756 m + 62.1 m =

17. Multiplying and Dividing Measurements
- The measurement with the fewest total significant figures determines the number of significant figures in the answer.

18. Examples: Solve using correct significant figures:
3.43 m X m =
m X m =
45.01 m / m =
22.0 m2 m2
55 m2 m2
20. m2