podane rozwinięcia dziesiętne zapisz w postaci ułamków zwykłych:
a) 0.(7)
b) 0.(13)
c) 0.(01)
a)
x=0,777...
10x=7,777..
10x-x=7,777...-0,777...
9x=7
x=7/9
b)
x=0,1313...
100x=13,1313...
100x-x=13,1313...-0,1313...
99x=13
x=13/99
c)
x=0,0101...
100x=1,0101...
100x-x=1,0101...-0,0101...
99x=1
x=1/99
a)77,77...=100x
-(7,77... = 10x)
-----------------------------
70=90x
b)1000x=131,31...
-(10x=1,31...)
----------------------------
990x=130
c)1000x=10,101...
-(10x=0,101...)
-------------------------------
990x=10
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a)
x=0,777...
10x=7,777..
10x-x=7,777...-0,777...
9x=7
x=7/9
b)
x=0,1313...
100x=13,1313...
100x-x=13,1313...-0,1313...
99x=13
x=13/99
c)
x=0,0101...
100x=1,0101...
100x-x=1,0101...-0,0101...
99x=1
x=1/99
a)77,77...=100x
-(7,77... = 10x)
-----------------------------
70=90x
x=7/9
b)1000x=131,31...
-(10x=1,31...)
----------------------------
990x=130
x=13/99
c)1000x=10,101...
-(10x=0,101...)
-------------------------------
990x=10
x=1/99