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When using a calculator, do all of the operations with as much precision as the calculator allows, and then round the result to the correct number of significant digits The correct number of significant digits in the result depends on the measurements and on the operation Addition and subtraction Look at the digits to the right of the decimal point Round the result to the least precise value among the measurements the smallest number of digits to the right of the decimal points Example: Add 1456 m, 41 m, and 203 m The least precise values are 41 m and 203 m because they have only one digit to the right of the decimal points 1456 41 203 25856 m m m m



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Multiplication and division Look at the number of significant digits in each measurement Perform the calculation Round the result so that it has the same number of significant digits as the measurement with the least number of significant digits Example: Multiply 201 m by 36 m (201 m)(36 m) 7236 m2 The least precise value is 36 m with two significant digits The product can only have as many digits as the least precise of the multiplied numbers 72 m

Answer Notes: It s legal for inner classes to implement interfaces, have constructors, and have initialization blocks 44 Given:





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500 Mobile, emergency, portable, and marine antennas The line flattener (Fig 25-15) is a standard transmatch antenna tuner that flattens coaxial-cable transmission line for VSWR This type of tuner is especially useful for transmitters with solid-state finals that are not happy with high VSWR Some of those designs incorporate shutdown circuits that reduce (and then cut off) power as the VSWR increases The line flattener basically tunes out the VSWR at the transmitter It does nothing to tune the antenna, but only makes the transmitter operable

Combination When doing a calculation that requires a combination of addition/ subtraction and multiplication/division, use the multiplication/division rule Examples: d ( 100 m/s2 )(250 s)2 19 m (250 m/s)(250 s) 2 1m 19 m only has two significant digits, so the answer should only 50 10

26 s and 11 s only have two significant digits each, so the answer should only have two significant digits

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Multistep calculations Do not round to significant digits in the middle of a multistep calculation Instead, round to a reasonable number of decimal places that will not cause you to lose significance in your answer When you get to your final step where you are solving for the answer asked for in the question, you should then round to the correct number of significant digits Example: F (24 N)2 576 N2 1872 N2 43 N (36 N)2 1296 N2

2 public class Later { 3 public static void main(String[] args) { 4 boolean earlyExit = new Later()test1(args); 5 if(earlyExit) assert false; 6 new Later()test2(args); 7 } 8 boolean test1(String[] a) { 9 if (alength == 0) return false; 10 return true; 11 } 12 private void test2(String[] a) { 13 if (alength == 2) assert false; 14 } }

Do not round to 580 N2 and 1300 N2 Do not round to 1800 N2 Final answer, so it should be rounded to two significant digits

A fraction names a part of a whole or a part of a group A fraction also can express a ratio (see page 838) It consists of a numerator, a division bar, and a denominator

Simplification Sometimes, it is easier to simplify an expression before substituting the known values of the variables Variables often cancel out of the expression Example: Simplify

difficulties for the antenna Of course, the first thing that springs to mind is the large size of those antennas A half-wavelength dipole is between 117 and 133 ft long on 75/80 m, and on 160 m it is about twice that length On my own suburban lot, I cannot erect a half-wave 75/80-m band antenna and stay within the property lines A similar situation is seen with vertical antennas Although a 40-m vertical (33 ft high) is not an unreasonable mechanical job, the 66 ft 75/80-m vertical (never mind the 120-ft 160-m vertical) is a nightmare In addition, the local authorities might not require any special inspections or permits (check!) on the 33-ft antenna, yet impose rigid and very exacting requirements on the higher structure On suburban or urban lots, a typical 40-m antenna might well be able to fall over and still not cross the property line or come in close proximity to power lines A longer antenna, however, almost inevitably suffers one or the other problem when it falls

Factor out the p in the numerator and the denominator, and break the fraction into the product of two fractions Substitute ( p/p) 1

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