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**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

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**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

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**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

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**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:

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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

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**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

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**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 ≈

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**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

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**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

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**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

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**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

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