concept development: real numbers imaginary...

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!

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

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

NAME:___________________________ Math_______,Period____________

Mr.Rogove Date:__________

G8M7L6:RationalNumbers4

Independent Practice: RewriteUsingthePowersof10andrepresentonanumberline

0. 573

0.985

0. 1422

0.14159

NAME:___________________________ Math_______,Period____________

Mr.Rogove Date:__________

G8M7L6:RationalNumbers5

Activating Prior Knowledge: Wecanrewritefractionsasdecimals

310!

1410!

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