Chapter 6

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Mathematics & Statistics (Sci)
MATH 111
Nabil Kahouadji

MATH 111 – Winter 2012 6: DECIMAL AND REAL NUMBERS 6.1 Introduction to Decimals - when converting fractions to decimals with tens, move the decimal the number of 0’s - ration number a/b in simplest form can be written as a terminating decimal if, and only if, the prime factorization of denominator contains no primes other than 2 or 5 6.1.1 Ordering Terminating Decimals 6.2 Operations on Decimals 6.2.1 Addition Decimals 6.2.2 Subtraction Decimals 6.2.3 Multiplying Decimals - multiplying by 10 = move decimal n positions to the right 6.2.4 Dividing Decimals - dividing by 10 = move decimal n positions to the left 6.2.5 Rounding Decimals 6.3 Nonterminating Decimals 6.3.1 Repeating Decimals - 3/11 is not a terminating decimals because 3/11 is in simplest form 6.3.2 A Surprising Result 6.3.3 Ordering Repeating Decimals 6.4 Real Numbers - every rational number is either terminating or repeating - some have decimal representation that neither terminates nor repeats - to find, focus on characteristics they must have: - infinite number of nonzero digits to the right of decimal points - can’t be a repeating block of digits - famous/important real numbers: square root of 2 a
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