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Chapter 1
Chapter 1

...  Adding two positive integers: Add the digits and keep the sign  Adding two negative integers: Add the digits and keep the sign  Adding a positive and a negative integer: Subtract the smaller from the larger digit (disregarding the signs) and keep the sign of the larger digit (if the sign is disr ...
Integer Addition and Subtraction
Integer Addition and Subtraction

Significant Figure Rules
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... There are three rules on determining how many significant figures are in a number: 1. Non-zero digits are always significant. 2. Any zeros between two significant digits are significant. 3. A final zero or trailing zeros in the decimal portion ONLY are significant. Focus on these rules and learn the ...
PPTX
PPTX

... • I have come to the conclusion that no, you cannot be onethird Scottish. I will provide my reasoning with the following two examples. Say there are two progenitors, P and Q. P is Korean and Q is American. If P and Q have a child, PQ, he will be 1/2 Korean and 1/2 American. Now say that PQ grows up ...
Excellence In All We Do…
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... is £28. All seats are full. Estimate how much it will cost to take all ...
- Math Express 99
- Math Express 99

... 2. The collection : 0 , 1, 2, 3, ……….. is called the collection of non-negative integers.. This is same as collection of whole numbers. 3. Integers can be represented on a number line. All integers to right of 0 are positive integers and those to left of 0 are negative integers. 4. Collection of int ...
Mathematics Name: Class: Real Numbers SECTION – A( 1 mark
Mathematics Name: Class: Real Numbers SECTION – A( 1 mark

... 1. .Prove that 3  5 is an irrational number. 2. Prove that 2 3 - 4 is an irrational number. 3. Prove that the square of any positive integer is of the form 3m or 3m + 1 for some integer m. 4. Prove that 3 - 5 is an irrational number. 5. Use Euclid’s division lemma to show that cube of any positive ...
Accuracy and Precision SIGNIFICANT FIGURES
Accuracy and Precision SIGNIFICANT FIGURES

... 1) Zeros in the middle of a numbers are significant figures. E.g. 4023 mL has 4 significant figures. 2) Zeros at the beginning of a number are not significant; they act only to locate the decimal point. E.g. 0.00206L has 3 significant figures. The zeros to the left of 2 are not sig. fig. 3) Zeros at ...
Direct Proof More Examples Contraposition
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... Since 3n + 2 = 2(3k + 1) we know that 3n + 2 is even. However, we are given that 3n + 2 is odd. This is a contradiction. Therefore our assumption that n is even must be incorrect. Therefore when 3n + 2 is odd, n must be odd. 2. Prove: No integer is both even and odd. Proof: Assume there exists some ...
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Addition and Subtraction of Fractions

... _____________________________________________________________________________________ Read pages 247 and 248 and then answer me this: Why do we simply add numerators when the denominators are the same? _____________________________________________________________ ____________________________________ ...
Azijas, Klus¯a oke¯ana olimpi¯ade, Skaitl¸u teorija
Azijas, Klus¯a oke¯ana olimpi¯ade, Skaitl¸u teorija

... a1 a2 a3 b1 , b2 , b3 , ..., bk of rational numbers, where ai , bi are relatively prime positive integers for each i = 1, 2, ..., k such that the positive integers a1 , b1 , a2 , b2 , ..., ak , bk are all distinct. APMO2009.5: Larry and Rob are two robots travelling in one car from Argovia to Zillis ...
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TOPIC 1 Work with numbers

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... A similar scheme can be used for square root[7]. We start with the input value A and a rst guess Y = 0. For each bit we compute the residual, R = A Y . Inspection of R at the k'th step is used to select a value for the k'th bit of Y . The selection rules give some exibility in tuning the algorithm ...
ppt - Andrew.cmu.edu
ppt - Andrew.cmu.edu

... representable would be 2-bias, which is not that small. And it would be represented by 000 00. Hmm… IEEE uses a trick to give us numbers closer to 0: drop the implied leading 1. ...
Chapter 5: Understanding Integer Operations and Properties
Chapter 5: Understanding Integer Operations and Properties

... • Adding two positive integers: Add the digits and keep the sign • Adding two negative integers: Add the digits and keep the sign • Adding a positive and a negative integer: Subtract the smaller from the larger digit (disregarding the signs) and keep the sign of the larger digit (if the sign is disr ...
Chapter 1
Chapter 1

...  Adding two positive integers: Add the digits and keep the sign  Adding two negative integers: Add the digits and keep the sign  Adding a positive and a negative integer: Subtract the smaller from the larger digit (disregarding the signs) and keep the sign of the larger digit (if the sign is disr ...
math-g5-m1-topic-d
math-g5-m1-topic-d

... module, students begin to use base ten understanding of adjacent units and whole number algorithms to reason about and perform decimal fraction operations—addition and subtraction in Topic D, multiplication in Topic E, and division in Topic F (5.NBT.7). In Topic D, unit form provides the connection ...
CompOrgW3LArith Floa..
CompOrgW3LArith Floa..

... is achieved, we see that before any calculating, the number must be unpacked from the form it takes in storage. The exponent and the fraction must be extracted, the arithmetic done, and then the result renormalized and rounded, and the bit patterns repacked into the required format. With FP format h ...
RN-coding of numbers: definition and some
RN-coding of numbers: definition and some

... representations. It is well-known that in radix β ≥ 2, every integer (real number) can be represented by a finite (infinite) digit chain, with digits in the digit set {−a, −a + 1, . . . , +a − 1, +a}, provided that 2a + 1 ≥ β. If 2a + 1 ≥ β + 1 then some numbers can be represented in more than one w ...
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10/20/04

... • Integer overflow error – Trying to represent an integer that is larger than the most positive allowable integer or more negative than most negative integer – Frequently occurs during math operations ...
Divisibility Rules
Divisibility Rules

... Use the same rule for rounding whole numbers—0, 1, 2, 3, 4 stays the same as it did before; 5, 6, 7, 8, 9 goes up one every time!  The rule number is the # to the immediate right of the number being rounded  The rule number will become a 0 with all other number to the right of the number that was ...
07. Decimals - IntelliChoice.org
07. Decimals - IntelliChoice.org

... Rounding off is a kind of estimating. Look at the digit to the right of the “rounding digit”. If the digit is 5 or more, round up by adding one to the rounding digit and drop all digits to the right of it; otherwise, do not change the rounding digit but drop all digits to the right of it. ...
Decimals
Decimals

... Converting decimals to fractions: Count how many numbers are behind the decimal. The fraction is form by placing the digits that were behind the decimal in the numerator and putting 1 followed by as many zeros as digits behind the decimal in the denominator. Remember to reduce the fraction. ...
2-DSP Fundamentals
2-DSP Fundamentals

... When defining a system in term of its coefficients, the finite precision affect the behavior of the system itself. Though there is a grid of possible locations where system’s poles can be placed. This grid depends first of the word-length and second of the structure adopted to implement of the syste ...
5-1
5-1

... 5.1.4.4.2. Definition of Integer Subtraction: For all integers a, b, and c, a – b = c if and only if c + b = a 5.1.4.4.3. Theorem: Subtracting an Integer by adding the Opposite – For all integers a and b, a – b = a + (-b). That is, to subtract an integer, add its opposite. 5.1.4.5. Procedures for Su ...
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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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