Question

Zapisz liczbe w postaci ulamka zwyklego;
a. 10,(05)
b. 11,(15)
c. 0,(1)
d. 10,(1) ;*

Answer 1

1005
------
100

1115
------
100

1
----
10

101
------
10

Answer 2

A)10całych i 5/100
b)11 całych i 15/100
c)1/10
d)10 całych i 1/10

Answer 3

A. 10,(05)

10.(05)=?
x=10.0505...
100x=1005.0505...
100x-x= 1005.0505...-10.0505...
99x=995
x= 995/99
x=10 5/99
10.(05)=10 5/99

b. 11,(15)= 11 5/33
11.(15)=?
x=11.1515...
100x=1115.1515...
100x-x= 1115.1515...-11.1515...
99x=1104
x=1104/99
x=11 15/99
x=11 5/33
11.(15)=11533

c. 0,(1) = 1/9
0.(1)=?
x=0.11...
10x=1.11...
10x-x= 1.11...-0.11...
9x=1
x=1/9
0.(1)=1/9

d. 10,(1) = 10 1/9

10.(1)=?
x=10.11...
10x=101.11...
10x-x= 101.11...-10.11...
9x=91
x=91/9
x=10 1/9
10.(1)=10 1/9