[...]... easily, as shown below: (1. 246 ϫ 10 4) ϫ (2.573 ϫ 10 –4) ϭ 3.206 ϫ 10 0 ϭ 3.206 (Note: 10 0 ϭ 1) (1. 785 ϫ 10 7) Ϭ (1. 039 ϫ 10 –4) ϭ (1. 785 /1. 039) ϫ 10 7–(–4) ϭ 1 718 ϫ 10 11 (1. 447 ϫ 10 5)2 ϭ (1. 447)2 ϫ 10 10 ϭ 2.094 ϫ 10 10 1. 3 91 ෆ08 ϭ 1. 3 911 /2 ϫ 10 8/2 ϭ 1. 179 ϫ 10 4 ෆෆෆෆ × 1 ෆ In the preceding examples, you must use the standard algebraic rules for addition, subtraction, multiplication, and division of exponents... Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Walsh CH02 8/30/05 9 :11 PM Page 17 Source: McGraw-Hill Machining and Metalworking Handbook Chapter 2 Mathematics for Machinists and Metalworkers This chapter covers all the basic and special... 2 (16 ) + 1. 57(5.56 + 3 .12 ) + 2 (5.56 − 3 .12 )2 = 45.7 21 4 (16 ) Most of the equations shown in this Handbook are solved in a similar manner, i.e., by substituting known values for the variables in the equations and solving for the unknown quantity using standard algebraic and trigonometric rules and procedures Ratios and proportions If a/b ϭ c/d, then Downloaded from Digital Engineering Library @ McGraw-Hill. .. Machinists and Metalworkers 31 2 .1. 3 Important mathematical constants ϭ 3 .14 15926535898 1 radian ϭ 57.295779 513 082° 1 ϭ 0. 017 453292 519 9 radian 2R ϭ 360° R ϭ 18 0° e ϭ 2. 718 2 818 28 (base of natural logarithms) 2 .1. 4 Summary of trigonometric procedures for triangles There are four possible cases in the solution of oblique triangles: Case 1: Given one side and two angles: a, A, B Case 2: Given two sides and. .. 1. 5 Digital micrometer Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Walsh CH 01 8/30/05 8:39 PM Page 11 Modern Metalworking Machinery, Tools, and Measuring Devices Modern Metalworking Machinery, Tools, and Measuring Devices 11 ... (0 1) Ϫ sin (1 0) Ϫ cos (0–ϱ) ϩ tan (ϱ–0) ϩ cot (1 ϱ) Ϫ sec (ϱ 1) Ϫ csc y 0 y′ Quadrant I sin ϩ (0 1) cos ϩ (1 0) tan ϩ (0–ϱ) cot ϩ (ϱ–0) sec ϩ (1 ϱ) csc ϩ (ϱ 1) x Quadrant IV sin Ϫ (1 0) cos ϩ (0 1) tan Ϫ (ϱ–0) cot Ϫ (0–?) sec ϩ (ϱ 1) csc Ϫ (1 ϱ) Trigonometric laws The trigonometric “laws” show the relationships between the sides and angles of non-right-angle triangles or acute and obtuse triangles and. .. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Walsh CH02 8/30/05 9 :11 PM Page 33 Mathematics for Machinists and Metalworkers Mathematics for Machinists and Metalworkers 33 2 .1. 5 Powers-of -1 0 notation Numbers written in the form 1. 875... 56.785° ϫ 0. 017 4533 ϭ 0.9 911 radian Example: Convert 2.0978R to decimal degrees 57.2957795 ϫ 2.0978 ϭ 12 0.05 91 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Walsh CH02 8/30/05 9 :11 PM Page 31 Mathematics for Machinists and Metalworkers... Machinists and Metalworkers 27 Figure 2.7 Solve the triangle Then angle B ϭ 18 0° Ϫ (angle A ϩ 90°) ϭ 18 0° Ϫ 12 3 .16 2° ϭ 56.838° We now know sides a, b, and c and angles A, B, and C Solving non-right-angled triangles using the trigonometric laws Solve the triangle in Fig 2.8 given two angles and one side: A ϭ 45° B ϭ 10 9° a ϭ 3.250 First, find angle C: Angle C ϭ 18 0° Ϫ (angle A ϩ angle B) ϭ 18 0° Ϫ (45° ϩ 10 9°)... written in the form 1. 875 ϫ 10 5 or 3.452 ϫ 10 Ϫ6 are so stated in powers-of -1 0 notation Arithmetic operations on numbers that are either very large or very small are processed easily and conveniently using the powers-of -1 0 notation and procedures If you will note, on the handheld scientific calculator this process is carried out automatically by the calculator If the calculated answer is larger or smaller . McGraw-Hill machining and metalworking handbook / Ronald A. Walsh. and Denis R. Cormier 3rd ed. p . cm. ISBN 0-0 7 -1 4578 7-9 1. Machining Handbooks, manuals, etc. 2. Metal-work—Handbooks, manuals,. are provided in Table 1. 2. Powder metallurgy. Metal powder is compacted by a die and then sintered to hold its shape. The resulting parts are porous and option- ally are infiltrated to 10 0 percent. that perform facing, knurling, grooving, boring, and many other turning operations. Electric discharge machining (EDM). EDM comes in two forms—sinker EDM and wire EDM. Sinker EDM uses spark erosion