1.5 Significant Figures A. Determining Significant Figures Rules for Zero: Rule 1: A zero counts as a significant figure when it occurs: • between two nonzero digits 29.05 g 4 sig. figures 1.0087 mL 5 sig. figures • at the end of a number with a decimal place 3.7500 cm 5 sig. figures 620. lb 3 sig. figures 29
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1.5 Significant Figures A. Determining Significant Figures Rules for Zero: Rule 1: A zero counts as a significant figure when it occurs: • between two nonzero digits 29.05 g 4 sig. figures 1.0087 mL 5 sig. figures • at the end of a number with a decimal place 3.7500 cm 5 sig. figures 620. lb 3 sig. figures 28
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Significant Figures (continued) We need rules to determine the number of significant figures in a given measurement. 3. 4. Zeros to the right of the rightmost nonzero digit (typically called trailing zeros) are significant. Ex. 9876.000 cm (7 significant figures)  Note: a decimal point is mandatory for #3 to be true. Otherwise the number of significant figures is ambiguous. Ex. 98,760 cm (?? significant figures) Zeros between two nonzero digits are significant. Ex. 9.800076 cm (7 significant figures) Copyright © McGraw-Hill Education. Permission required for reproduction or display. 1-105
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From the simple color demo: // object with all faces having the same color var triGeom1 = createTriGeometry(size); var triMaterial = new THREE.MeshBasicMaterial( {color: new THREE.Color(“blue”)} ); var triMesh1 = new THREE.Mesh(triGeom1, triMaterial); scene.add(triMesh1); // object with each face having a different color var triGeom2 = createTriGeometry(size); var triMaterials = new THREE.MeshFaceMaterial ( [new THREE.MeshBasicMaterial({color: new THREE.Color(“red”)}), new THREE.MeshBasicMaterial({color: new THREE.Color(“green”)}), new THREE.MeshBasicMaterial({color: new THREE.Color(“cyan”)}), new THREE.MeshBasicMaterial({color: new THREE.Color(“magenta”)}) ]); triGeom2.faces[0].materialIndex = 0; // but now for something different – suppose we want faces 1,2,3 to be cyan TW.setMaterialForFaces(triGeom2, 2, 1, 2, 3); // 2nd input is index of desired material var triMesh2 = new THREE.Mesh(triGeom2, triMaterials);
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Rules for Counting Significant Figures 1. All nonzero integers are significant figures; Examples: 453.6 has four significant figures; 4.48 x 105 has three significant figures; 0.00055 has two significant figures.
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1-4 Significant Figures Scientific Notation • Leading or trailing zeroes can make it hard to determine number of significant figures: 2500, 0.000036 • Each of these has two significant figures • Scientific notation writes these as a number from 1-10 multiplied by a power of 10, making the number of significant figures much clearer: 2500 = 2.5 × 103 If we write 2.50x103, it has three significant figures 0.000036 = 3.6 x 10-5
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1.5 Significant Figures A. Determining Significant Figures Rules for Zero: Rule 2: A zero does not count as a significant figure when it occurs: • at the beginning of a number 0.00245 mg 3 sig. figures 0.008 mL 1 sig. figure • at the end of a number that does not have a decimal 2570 m 3 sig. figures 1245500 m 5 sig. figures 30
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1.5 Significant Figures A. Determining Significant Figures Rules for Zero: Rule 2: A zero does not count as a significant figure when it occurs: • at the beginning of a number 0.00245 mg 3 sig. figures 0.008 mL 1 sig. figure • at the end of a number that does not have a decimal 2570 m 3 sig. figures 1245500 m 5 sig. figures 29
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1.5 Significant Figures  A. Determining Significant Figures Rules for Zero: Rule 1: A zero counts as a significant figure when it occurs: •between two nonzero digits 29.05 g 4 sig. figures 1.0087 mL 5 sig. figures •at the end of a number with a decimal place 3.7500 cm 5 sig. figures 620. lb 3 sig. figures 25
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1.5 Significant Figures  B. Rules for Multiplication and Division The answer has the same number of significant figures as the original number with the fewest significant figures. 4 sig. figures 351.2 miles = 5.5 hour 2 sig. figures 63.854545 miles hour Answer must have 2 sig. figures. 27
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Rules for Counting Significant Figures 2. Captive zeroes – (zeroes between nonzero digits) are significant figures. Examples: 1.079 has four significant figures; 1.0079 has five significant figures; 0.08206 has four significant figures.
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Rules for Counting Significant Figures 4. Trailing zeroes – these are zeroes at the right end of the number. They are counted as significant figures if the number contains a decimal point, otherwise it is not counted. Examples: 208.0 has 4 significant figures; 2080. also has 4 significant figures, but 2080 has 3 significant figures;
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Calculations with Measured Numbers In calculations with measured numbers, significant figures or decimal places are counted to determine the number of figures in the final answer. Multiplication and Division When multiplying or dividing use  The same number of significant figures as the measurement with the fewest significant figures.  Rounding to obtain the correct number of significant figures. Example: 110.5 4 SF S-10 x 0.048 = 5.304 2 SF = calculator 5.3 (rounded) 2 SF AVC-CHEM-CH 21
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Multiplication and Division Round the calculated answer so that it contains the same number of significant figures as the measurement with the least number of significant figures. In other words, if the measurement with the least number of significant figures contains two significant figures, then the rounded answer should contain two significant figures.
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Suppose the variables A,B,C,D are each assigned to a new THREE.Vector3 object with the desired x,y,z coordinates 2, C, blue 3, D, red colors = [new THREE.Color(TW.RED), new THREE.Color(TW.LIME), new THREE.Color(TW.BLUE), new THREE.Color(TW.RED)]; triGeom = new THREE.Geometry(); triGeom.vertices = [A, B, C, D]; triGeom.faces = [new THREE.Face3(0,1,2), 0, A, red 1, B, lime new THREE.Face3(2,1,3); triGeom.vertexColors = colors; TW.computeFaceColors(triGeom); var material = new THREE.MeshBasicMaterial( {vertexColors: THREE.VertexColors} ); var mesh = new THREE.Mesh(triGeom, material); scene.add(mesh);
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