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

Counting Significant Figures, Continued 4) Leading zeros (on the left of a number) are NOT significant. 0.001050 has 4 significant figures. 1.050 x 10-3 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. 542,000,000 has 3 significant figures. Tro's "Introductory Chemistry", Chapter 2

Tro's "Introductory Chemistry", Chapter 2 Practice: How many significant figures are in each of the following numbers? a) 0.0035--- b) 1.080--- c) 2371--- d) 2.97 × 105--- e) 100,000--- 2 sig. fig.—leading zeros are not significant. (Rule #4). 4 sig. fig.—zeros after the decimal & interior zeros are significant. (Rule #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

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: 2.536 --- 2.54 b) lesser than 5 – Do NOT round up: 2.532 ---- 2.53 c) equal to 5:

c) equal to 5: 1) followed by a non-zero –ROUND UP: 2.5351 --- 2.54 2) followed by zero: If the last significant figure: - is an odd digit – ROUND UP: 2.5350 --- - is an even digit– Do NOT round up: 2.5250 ---- 2.52

Tro's "Introductory Chemistry", Chapter 2 Rounding to 2 significant figures: 2.34 rounds to: 2.3 2.37 rounds to: 2.4 2.349865 rounds to: 0.0234 rounds to: 0.023 or 2.3 × 10-2 0.0237 rounds to: 0.024 or 2.4 × 10-2 Tro's "Introductory Chemistry", Chapter 2

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: 28.0 cm + 23.538 cm 25.68 cm 77.218 cm ≈

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: 28.0 cm + 23.538 cm 25.68 cm 77.218 cm ≈ 77.2 cm

Tro's "Introductory Chemistry", Chapter 2 Practice: 1) 5.74 + 0.823 + 2.651 = 2) 4.8 - 3.965 = 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

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

Tro's "Introductory Chemistry", Chapter 2 Practice: 1) 5.02 × 89,665 × 0.10 = 2) 5.892 ÷ 6.10 = 3) 1.01 × 0.12 × 53.51 ÷ 96 = 4) 56.55 × 0.920 ÷ 34.2585 = 45.0118 = 45 3 sig. figs. 5 sig. figs. 2 sig. figs. 0.96590 = 0.966 4 sig. figs. 3 sig. figs. 0.06775 = 0.068 3 sig. figs. 4 sig. figs. 2 sig. figs. 2 sig. figs. = 1.52 1.51863 4 sig. figs. 3 sig. figs. 6 sig. figs. Tro's "Introductory Chemistry", Chapter 2