SMART Packet #2 Determing the Relative Error
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1 Unit 3: Geometric Formulas SMART Packet #2 Determing the Relative Error Student: Teacher: Standards A.M.3 Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure
2 REMINDER: This means take the absolute value! Example 1: Ryan estimates the measurement of the volume of a popcorn container to be 282 cubic inches. The actual volume of the popcorn container is 289 cubic inches. What is the relative error of Ryan's measurement to the nearest thousandth? Solution: The measured value of the volume is 282 cubic inches. The actual value of the volume is 289 cubic inches. Hence, HINT: Round to the nearest thousandth!
3 Practice Problems (Part I): 1. Carrie bought new carpet for her living room. She calculated the area of the living room to be square feet. The actual area was square feet. What is the relative error of the area to the nearest ten-thousandth? The measured value of the area is square feet. The actual value of the area is square feet. Hence, 2. A student determined the density of zinc to be 6.63 g/cm3. The correct value is 7.13 g/cm3. Find the relative error in her measurement.
4 3. To calculate the volume of a small wooden cube, Ezra measured an edge of the cube as 2 cm. The actual length of the edge of Ezra s cube is 2.1 cm. What is the relative error in his length calculation to the nearest hundredth? Sometimes, one or two extra steps are required (e.g. you could be given lengths but asked to find relative error in area or volume).
5 Example 2: Sarah measures her rectangular bedroom window for a new shade. Her measurements are 36 inches by 42 inches. The actual measurements of the window are 36.5 inches and 42.5 inches. Using the measurements that Sarah took, determine the number of square inches in the area of the window. Determine the number of square inches in the actual area of the window. Determine the relative error in calculating the area. Express your answer as a decimal to the nearest thousandth. Solution: The measured area is The actual area is Hence, square inches. square inches.
6 Practice Problems (Part II): 1. A box has the measurements 1.4 cm by 8.2 cm by 12.5 cm. When Joe measured the box, he found that it was 1 cm by 8 cm by 13 cm. Find the relative error in Joe's calculated volume. The measured volume is x x = cubic cm. The actual volume is x x = cubic cm. Hence, 2. A student measures the side of a cube and accidentally reads a length of 5 inches, when the real length is 6 inches. What will be the relative error when she calculates the cube's volume?
7 3. The groundskeeper is replacing the turf on a football field. His measurements of the field are 130 yards by 60 yards. The actual measurements are 120 yards by 54 yards. What will is his relative error in the measurement of the field's area? Practice Problems (Part III): 1. Sophie measured a piece of paper to be 1.7 cm by 28.5 cm. The piece of paper is actually 21.6 cm by 28.4 cm. Determine the number of square centimeters in the area of the piece of paper using Sophie s measurements. Determine the number of square centimeters in the actual area of the piece of paper. Determine the relative error in calculating the area. Express your answer as a decimal to the nearest thousandth. Sophie does not think there is a significant amount of error. Do you agree or disagree? Justify your answer.
8 2. A student determines the density of a mineral to be 1.5 grams per cubic centimeter. If the accepted value is 2.0 grams per cubic centimeter, what is the student s relative error? 3. A student incorrectly measured the volume of a mineral sample as 83 cubic centimeters when the actual volume was 89 cubic centimeters. What was the student s relative error?
9 4. (a) A student mistakenly measures the length of a radius to be 24 inches. The actual radius is 25 inches. (b) If the student uses this measurement to compute the area of a circle with this radius, what is the student's relative error on the area computation, to the nearest tenth.
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Student Activity #1 String, Tiles, and Cubes Name Directions: For this activity, your team will be measuring attributes of different objects and shapes. You will record your findings in an organized chart.
Extra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million b) 6 billion c)
Master 4.27 Extra Practice 1 Lesson 1: Numbers in the Media 1. Rewrite each number in standard form. 3 a) 3.6 million b) 6 billion c) 1 million 4 2 1 d) 2 billion e) 4.25 million f) 1.4 billion 10 2. Use