Question

transforme as dizimas periódicas em fração:
a) 0,345..
b)2,45..
c)0,333..
d)2,7..
e)0,(45)
f)0,2(4)
g)0,0(35)
h)0,1(63)
i)0,375..
j)0,579..
k)0,49974997
l)1,6363

Answer 1

a) 345/999
b) 243/99
c) 3/9
d) 25/9
e) 45/99
f) 22/90
g) 32l900
h) 162/990
i) 375/999
j) 579/999
k) 4997/9998
l) 162/99.

Answer 2

A) x = 0,345...
1000x = 345,345...

1000x-x = 345,345...-0,345...
999x = 345
x = 345/999
x = 115/333

B) x = 2,45...
100x = 245,45...

100x - x = 245,45... - 2,45...
99x = 243
x = 243/99
x = 81/33

C) x = 0,3...
10x = 3,3...

10x - x = 3,3... - 0,3...
9x = 3
x = 3/9
x = 1/3

D) x = 2,7...
10x = 27,7...

10x-x= 27,7... - 2,7...
9x = 25
x = 25/9

E) x = 0,(45) = 0,45...
100x = 45,45...

100x-x = 45,45... - 0,45...
99x = 45
x=45/99
x=5/11

F) x = 0,2(4) = 0,2444...
10x = 2,4...
100x = 24,4...

100x - 10x = 24,4... - 2,4
90x = 22
x = 22/90
x = 11/45

G) x = 0,0(35)
10x = 0,(35)
1000x = 35,(35)

1000x - 10x = 35,(35) - 0,(35)
990x = 35
x = 35/990
x = 7/168

H) x = 0,1(63)
10x = 1,(63)
1000x = 163,(63)

1000x - 10x = 163,(63) - 1,(63)
990x = 163
x = 163/990
x = 9/55

I) x = 0,(375)
1000x = 375,(375)

1000x - x = 375,(375) - 0,(375)
999x = 375
x = 375/999
x = 125/333

J) x = 0,(579)
1000x = 579,(579)

1000x - x = 579,(579) - 0,(579)
999x = 579
x = 579/999
x = 193/33

K) x = 0,(4997)
10000x = 4997,(4997)

10000x - x = 4997,(4997) - 0,(4997)

9999x = 4997
x = 4997/9999


L) x = 1,(63)
100x = 163,(63)

100x - x = 163,(63) - 1,(63)
99x = 162
x = 162/99
x = 18/11