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CS321 Introduction to Numerical Methods
CS321 Introduction to Numerical Methods

... With normalized representation, the first bit is always 1 and needs not be stored. The mantissa actually contains 24 binary digits with a hidden bit With a mantissa of 23 bits, a machine can have about six significant decimal digits of accuracy, since 2 −23 ≈ 1.2 ×10 −7 The smallest positive number ...
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... 14) You get into an elevator on the 7th floor. The elevator goes down 5 floors, up 12 floors, down 9 floors, then back up two floors, where you exit the elevator. What floor are you on now? Show 2 methods for solving for your new location. ...
2015 High School Math Contest - Wisconsin Mathematics Council
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... [Reduce all common fractions. Simplify and rationalize denominators. Unless otherwise specified, a decimal approximation will not be accepted. When allowed, round decimal approximations to 3 decimal places. No rounding should be done except on the final answer.] For this first problem set, calculato ...
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... can measure. The last digit in a number is always assumed to be uncertain. If we measure something and get 10.34 cm, we are really saying that we are sure about the 10.3 cm, but we are estimating the 4. So our measurement is between 10.33 cm and 10.35 cm. Or, 10.34cm (+/-) 0.01 cm ...
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... • When first identifying significant numbers, zeros at the beginning or end don’t usually count, but zeros ‘inside’ the number do. • Digits of a number kept in place by zeros where necessary. • The rounded answer should be a suitable reflection of the original number e.g. 24,579 to 1 s.f could not p ...
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... Fraction [frœkš n] is a ratio of numbers or variables. ...
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... Scientific notation is a method of writing numbers that are very small or large. A number written in scientific notation has two parts that are multiplied. One is the base – which must be a number greater than or equal to 1, and less than 10; and the other is a power of 10: ...
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Y5 A1 mental quick maths

... 3. The smallest four digit number using the digits 5,9,0,6 is 5096. 4. The smallest five digit number using the digits 4, 9, 0 is 40009. 5. The smallest three digit number using the digits 1, 9, 6 is 169. ...
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... • Once you have determined how many significant figures is in your answer, there are a few rules for rounding off: 1. Round down if the digit to be removed is less than 5. 1.33 rounded to two significant figures becomes 1.3 ...
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... 2 hours and 15 minutes. If she travels downhill at 24 km/h, on level road at 16 km/h and uphill at 12 km/h, what is the distance, in kilometres, between the two towns? 11. The first and second terms of a sequence are 4 and 5, respectively. Each term after the second is determined by increasing the p ...
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... iquo, irem, mod, numer, round, sign, trunc The first thing to keep in mind about Maple is that it prefers to work with numbers exactly, rather than with approximations. Hence, if we enter O t d sqrt 5 ; t := 5 ...
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... When you use an analytical balance you will see: (Example: 4.1236 g has 5 s.f., the last digit is uncertain!) III. The significant figures of Numbers: Identifying S. f.: 1) All non-zero digits, count as S.f. count as S.f. (Example: 128736, has 6 s.f.) 2) Captive Zeros (zeros between two non-zero dig ...
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... Max has 8 boxes of cans for a food drive. Each box has 17 cans. Max gives half of the boxes to his teacher. Write an expression that represents the total number of cans in all the boxes that his teacher ...
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... Third Piece -- The power of 2 that you got in the last step is simply an integer. Note, this integer may be positive or negative, depending on whether the original value was large or small, respectively. We'll need to store this exponent -- however, using the two's complement, the usual representati ...
SWilliams Carr Lesson 7 Practice Set C
SWilliams Carr Lesson 7 Practice Set C

... Students should be able to talk about the benchmarks and midpoints in order to show how they round their decimal number. Ex. In order to round to the nearest hundredth, we need to look at the 2.736 part of the decimal number. The nearest hundredth below 2.730 and above 2.740 help us to determine whi ...
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IEEE Floating Point Instructions

... Back to the example Our original example revisited…. 1.1011 * 22 Exponent is 2+127 =129 or 10000001 in binary. NOTE: Mantissa always ends up with a value of ‘1’ before the Dot. This is a waste of storage therefore it is implied but not actually stored. 1.1000 is stored .1000 6.75 in 32 bit floating ...
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Rounding

Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing £23.4476 with £23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement or estimate; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is better stated as ""about 123,500.""On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations — especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating point representation with a fixed number of significant digits. In a sequence of calculations, these rounding errors generally accumulate, and in certain ill-conditioned cases they may make the result meaningless.Accurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as ""the table-maker's dilemma"".Rounding has many similarities to the quantization that occurs when physical quantities must be encoded by numbers or digital signals.A wavy equals sign (≈) is sometimes used to indicate rounding of exact numbers. For example: 9.98 ≈ 10.
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