concept development: real numbers imaginary...

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NAME:___________________________ Math _______, Period ____________ Mr. Rogove Date:__________ G8M7L6: Rational Numbers 1 Learning Objective: We will differentiate between rational and irrational numbers. (G8M7L6) Concept Development: Real Numbers Imaginary Numbers Rational Numbers: Any number that can be expressed as a fraction ! ! where p and q are both integers and ! ≠ 0. Example: 4.3, ! ! , − ! !"# , 68. 9 Finite Decimals: A subset of rational numbers which have terminating decimals. Written as fractions, the denominators are products of only 2’s and 5’s. Example: ! !" , 1.05, 4.253 Repeating Decimals: A subset of rational numbers that have infinite decimals that repeat. Example: ! ! , !" !" , 0.4545454545 …. Irrational Numbers: The set of numbers that have infinite decimals that DO NOT repeat. Example: !, !, 8 , 25 !

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Page 1: Concept Development: Real Numbers Imaginary Numbersmrrogove.weebly.com/uploads/4/3/0/0/43009773/g8m7l6-_rational_and... · NAME:_____ Math _____, Period _____ Mr. Rogove Date:_____

NAME:___________________________ Math_______,Period____________

Mr.Rogove Date:__________

G8M7L6:RationalNumbers1

Learning Objective:Wewilldifferentiatebetweenrationalandirrationalnumbers.(G8M7L6)Concept Development:

RealNumbers

ImaginaryNumbers

RationalNumbers:Anynumberthatcanbeexpressedasafraction!!wherepandqarebothintegersand! ≠ 0.Example:4.3, !! , −

!!"# , 68. 9

FiniteDecimals:Asubsetofrationalnumberswhichhaveterminatingdecimals.Writtenasfractions,thedenominatorsareproductsofonly2’sand5’s.Example: !!" , 1.05, 4.253RepeatingDecimals:Asubsetofrationalnumbersthathaveinfinitedecimalsthatrepeat.Example:!! ,

!"!" , 0.4545454545….

IrrationalNumbers:ThesetofnumbersthathaveinfinitedecimalsthatDONOTrepeat.Example:!,!, 8, 25!

Page 2: Concept Development: Real Numbers Imaginary Numbersmrrogove.weebly.com/uploads/4/3/0/0/43009773/g8m7l6-_rational_and... · NAME:_____ Math _____, Period _____ Mr. Rogove Date:_____

NAME:___________________________ Math_______,Period____________

Mr.Rogove Date:__________

G8M7L6:RationalNumbers2

Guided Practice: StepsforConvertingFractionstoDecimals1.Determineifthefractionwillbeafiniteorarepeatingdecimal.2.Iffinite,multiplythefractionbyfactorsof2and5untilthedenominatorisequalto 2×5 ! = 10!.3.Rewritethefractionasadecimal.

4364

780

29125

3740

71250

15128

Page 3: Concept Development: Real Numbers Imaginary Numbersmrrogove.weebly.com/uploads/4/3/0/0/43009773/g8m7l6-_rational_and... · NAME:_____ Math _____, Period _____ Mr. Rogove Date:_____

NAME:___________________________ Math_______,Period____________

Mr.Rogove Date:__________

G8M7L6:RationalNumbers3

StepsforRewritingDecimals(FiniteandInfinite)inExpandedFormUsingthePowersof101.Representeachdigitasanumberwithadenominatorthatisapowerof10.2.Determinethedecimalisfinite(terminating)orinfinite.3.Ifrequired,drawnumberlinestorepresentthedecimal.

0.253

0.3765

0.83

0. 83

Page 4: Concept Development: Real Numbers Imaginary Numbersmrrogove.weebly.com/uploads/4/3/0/0/43009773/g8m7l6-_rational_and... · NAME:_____ Math _____, Period _____ Mr. Rogove Date:_____

NAME:___________________________ Math_______,Period____________

Mr.Rogove Date:__________

G8M7L6:RationalNumbers4

Independent Practice: RewriteUsingthePowersof10andrepresentonanumberline

0. 573

0.985

0. 1422

0.14159

Page 5: Concept Development: Real Numbers Imaginary Numbersmrrogove.weebly.com/uploads/4/3/0/0/43009773/g8m7l6-_rational_and... · NAME:_____ Math _____, Period _____ Mr. Rogove Date:_____

NAME:___________________________ Math_______,Period____________

Mr.Rogove Date:__________

G8M7L6:RationalNumbers5

Activating Prior Knowledge: Wecanrewritefractionsasdecimals

310!

1410!

Closure: Doesthefraction!!! havearepeatingorterminatingdecimal?Howdoyouknow?Notes: ThismapstoLesson7and8fromModule7Grade8

Concept Development: Irrational Numbers: and DO NOTmrrogove2016.weebly.com/uploads/4/3/0/0/43009773/g... · Irrational Numbers: Numbers that have infinite decimal expansions and DO

Learning Objective: Activating Prior Knowledgemrrogove.weebly.com/uploads/4/3/0/0/43009773/g8m1l11...NAME:_____’ ’ Math_____’,Period_____’ Mr.Rogove’ ’ Date:_____’ 3’

Ludwigshafen - pfv.lbm-rlp.org · 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Learning Objective: Concept Developmentmrrogove.weebly.com/uploads/4/3/0/0/43009773/... · NAME:_____’ ’ Math7.1,Period’1and2’ Mr.Rogove’ ’ Date:_____’ 1’ Lesson’59:Raisingabase’to’the’zeroth’power’

Irrational Numbers Study Guide - mrrogove.weebly.commrrogove.weebly.com/.../3/0/0/43009773/irrational_numbers_study_g… · Irrational Numbers Study Guide ... ,!!!!!0.4545454545…

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1 - KROVNA KONSTRUKCIJA : OPTERE ĆENJE KROVNE KONSTRUKCIJE · σ = M / W σ = 12790 / 240 = 532,92 N / cm 2 σ < σd = 1000 N / cm 2 Usvajam rogove b / d = 10 / 12 . 1.2. ROŽNJA

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United States v. Jay Lewis Dworken, A/K/A Jason Lewis, Jay Lewis, United States of America v. William S. Gay, United States of America v. Steve Rogove, 855 F.2d 12, 1st Cir. (1988)

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