Operations with Significant Figures

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Presentation transcript:

Operations with Significant Figures Multiplication or Division Addition or Subtraction

Rule 1. When approximate numbers are multiplied or divided, the number of significant digits in the final answer is the same as the number of significant digits in the least accurate of the factors. Example 1: Least significant factor (45) has only two (2) digits so only two are justified in the answer. The appropriate way to write the answer is: P = 7.0 N/m2

Rule 2. When approximate numbers are added or subtracted, the number of significant digits should equal the smallest number of decimal places of any term in the sum or difference. Ex 2: 9.65 cm + 8.4 cm – 2.89 cm = 15.16 cm Note that the least precise measure is 8.4 cm. Thus, answer must be to nearest tenth of cm even though it requires 3 significant digits. The appropriate way to write the answer is: 15.2 cm

Classroom Example: A car traveling initially at 46 Classroom Example: A car traveling initially at 46.0 m/s undergoes constant acceleration of 2.0 m/s2 for a time of 4.30 s. Find total displacement, given formula. For class work, we assume all given info is accurate to 2 significant figures. d = 220 m

Two (9.0 has least significant digits). Lab Example 1: The length of a sheet of metal is measured as 233.5 mm and the width is 9.0 mm. Find the area. (Multiplication Rule) Note that the precision of each measure is to the nearest tenth of a millimeter. However, the length has four significant digits and the width has only two. How many significant digits are in the product of length and width (area)? Two (9.0 has least significant digits).

Lab Example 1 (Cont.): The length of a sheet of metal is measured as 233.5 mm and the width is 9.0 mm. Find area. Area = LW = (233.5 mm)(9.0 mm) Area = 2101.5 mm2 L = 233.5 mm W = 9.0 mm But we are entitled to only two significant digits. Therefore, the answer becomes: Area = 2100 mm2

Lab Example 2: Find the perimeter of sheet of metal, with measured L = 233.5 mm and W = 9.0 mm. (Addition Rule) P = 233.5 mm + 9.0 mm + 233.5 mm + 9.0 mm P = 485 mm L = 233.5 mm W = 9.0 mm Note: The answer is determined by the least precise measure. (the tenth of a mm) Note: The result has more significant digits than the width factor in this case. Perimeter = 485.0 mm