Numbers after the decimal point - Colegiul Ortodox "Mitropolitul Nicolae Colan" (Cluj-Roumanie)

Colegiul Ortodox "Mitropolitul Nicolae Colan" (Cluj-Roumanie)
When we do a division, sometimes it works out correctly:3/4=0,75
But most often, no: 1/3=0,3333333
We observe that a digit or a group of digits, repeats itself indefinitely. For what?
We can we predict the size of this group figures?
2.Experiment, make conjectures. Sometimes this repeating group of numbers is preceded by something not repeated:1/6=0,166666666, When does this happen? Conversely if we give ourselves a sequence of numbers that repeats, can we find a division. Who gives these numbers after the decimal point?
3. Calculate 1/7, 3/7, 2/7 in that order. What do we notice? Does it continue with other fractions? Can we construct other examples with the same examples with the same phenomenon? How explain it?
Type de présentation au congrès
À présenter
aux lycéens