Question

Witam potrzebuję o zapisanie liczb w postaci ułamków zwykłych

a) 13,2(4)

b) 1,2(7)

c) 3,2(6)

d) 2,3(2)

e) -3,12(6)

Chodzi mi o zrobienie tych przykładów taki oto sposobem:

a) x = -2,7777...

1000x = -2777,77...

100x = -277,777...

1000x - 100x = -2777,777.... + 277,777....

900x = -2500/:900

x = -2500/900

x = -25/9

To jest tylko przykład

Answer 1

a) 13,2(4) = x

x = 13,244444....

10x = 132,444...

100x = 1324,444...

100x - 10x = 1324,444...-132,444...

90x = 1192  /:90

x = 1192/90 = 596/45

 

b) 1,2(7) = x

x = 1,27777...

10x = 12,777...

100x = 127,777...

100x - 10x = 127,777...-12,777...

90x = 115

x = 115/90 = 23/18

 

c) 3,2(6) = x

x = 3,26666...

10x = 32,666...

100x = 326,666...

100x - 10x = 326,666...-32,666...

90x = 294

x = 294/90 = 147/45

 

d) 2,3(2) = x

x = 2,32222...

10x = 23,222...

100x = 232,222...

100x - 10x = 232,222...-23,222...

90x = 209

x = 209/90

 

e) -3,12(6) = x

x = -3,12666....

100x = -312,666...

1000x = -3126,666...

1000x - 100x = -3126,666...+312,666...

900x = -2814

x = -2814/900 = -1407/450