Question

Każdy z ułamków dziesiętnych przedstaw w postaci ułamka zwykłego.

a) 0,7(3)

b) 0,(145)

c) 0,41(6)

d) 0,(54)

e) 3,425(36)

Answer 1

a)
0,7(3)
x = 0,733...

100x = 73,333..
100x - 10x = 73,333.. - 7,333..
90x = 66/:90
x = 66/90
====================================

b)
0,(145)
x = 0,145

1000x = 145,145..
1000x - x = 145,145... - 0,145
999x = = 145/:999
x = 145/999
====================================

c) 0,41(6)
x = 0,416...

1000x = 416,666...
1000x - 100x = 416,666... - 41,666...
900x = 375/:900
x = 375/900
====================================

d)
0,(54)
x = 0,5454...

100x = 54,5454...
100x - x = 54,5454... - 0,5454...
99x = 54/:99
x = 54/99
====================================

e)
3,425(36)
x = 3,42536...

100000x = 342536,3636...
100000x - 1000x = 342536,3636.. - 3425,3636...
99000 = 339111/:99000
x = 339111/99000