Counting Significant Figures 1 All nonzero digits are

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Counting Significant Figures: 1) All non-zero digits are significant. – 1. 5 has 2

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 1

Counting Significant Figures, Continued 4) Leading zeros (on the left of a number) are

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 has 3 significant figures. Tro's "Introductory Chemistry", Chapter 2 2

Practice: • How many significant figures are in each of the following numbers? a)

Practice: • How many significant figures are in each of the following numbers? a) 0. 0035 --- 2 sig. fig. —leading zeros are not significant. (Rule #4). b) 1. 080 --- 4 sig. fig. —zeros after the decimal & interior zeros are significant. (Rule #2 & 3). c) 2371 --- 4 sig. fig. —all non zeros digits are significant (Rule #1). d) 2. 97 × 105 --- 3 sig. fig. —all non zeros digits are significant (Rule #1). e) 100, 000 --- 1 sig. fig. —zeros to the right of a # with out decimal point are not significant Tro's "Introductory Chemistry", Chapter 2 3

Rules for rounding numbers: 1) If the digit immediate right of the last significant

Rules for rounding numbers: 1) 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.

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 --2. 54 - is an even digit– Do NOT round up: 2. 5250 ---2. 52

 • • • Rounding to 2 significant figures: 2. 34 rounds to: 2.

• • • Rounding to 2 significant figures: 2. 34 rounds to: 2. 37 rounds to: 2. 4 2. 349865 rounds to: 2. 3 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 6

Rounding Rules in Addition & Subtraction: The result must be rounded up to the

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

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

1) 5. 74 + Practice: 0. 823 + 2. 651 = 9. 214 =

1) 5. 74 + Practice: 0. 823 + 2. 651 = 9. 214 = 9. 21 2 decimal 3 decimal places 2) 4. 8 - 1 decimal place 3. 965 = 0. 835 = 0. 8 3 decimal places Tro's "Introductory Chemistry", Chapter 2 9

Rounding Rules in Multiplication & Division: The answer must have the same number of

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 = 78. 72 ≈ 79 23. 5 x 1. 2 = 28. 2 ≈ 28 60. 2 ÷ 20. 1 = 2. 995 ≈ 3. 00

Practice: 1) 5. 02 × 3 sig. figs. 89, 665 × 0. 10 =

Practice: 1) 5. 02 × 3 sig. figs. 89, 665 × 0. 10 = 45. 0118 = 45 5 sig. figs. = 0. 96590 = 0. 966 2) 5. 892 ÷ 6. 10 4 sig. figs. 2 sig. figs. 3) 1. 01 × 0. 12 × 53. 51 ÷ 96 = 0. 06775 = 0. 068 3 sig. figs. 2 sig. figs. 4 sig. figs. 2 sig. figs. 4) 56. 55 × 0. 920 ÷ 34. 2585 = 1. 51863 = 1. 52 4 sig. figs. 3 sig. figs. 6 sig. figs. Tro's "Introductory Chemistry", Chapter 2 11