MATEMATYKA PROSTO DO MATURY 1, Nowa Era, nowa podstawa programowa
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Zapis dziesiętny liczby rzeczywistej
Zadanie 2.4./22 strona
Zapisz w postaci ułamka zwykłego
3,(15)=
11,(3)=
0,1(5)=
-2,0(1)=
-7,(8)=
13,2(4)=
5,3(2)=
17,(5)
1,2(6)=
3,2(9)=
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Zadanie 1.
3,(15)=3+0,(15)
0,(15)=x |*100
100x=15,(15)
100x=15+x
99x=15
x=15/99
3+15/99=3 i 15/99
3,(15) = 3 i 15/99
====================
11,(3)=11+0,(3)
0,(3)=x
10x=3,(3)
10x=3+x
9x=3
x=1/3
11 + 1/3 = 11 i 1/3
11,(3)=11 i 1/3
==================
0,1(5)=x
10x=1,(5)
1,(5)=y
1+0,(5)=y
0,(5)=z
10z=5,(5)
10z=5+z
9z=5
z=5/9
1 + 5/9 = y
y = 1 i 5/9 = 14/9
10x=14/9 |:10
x = 14/90
0,1(5)= 14/90
==================
-2,0(1)=x
-2-0,0(1)=x
0,0(1)=y
10y=0,(1)
0,(1)=z
10z=1,(1)
10z=1+0,(1)
10z=1+z
9z=1
z=1/9
10y=1/9 |:10
y=1/90
-2-1/90=x
x=-2 i 1/90
-2,0(1)= -2 i 1/90
===================
-7,(8)=x
-7-0,(8)=x
0,(8)=y
10y=8,(8)
10y=8+0,(8)
10y=8+y
9y=8
y=8/9
-7 - 8/9 = x
-7,(8) = -7 i 8/9
=====================
13,2(4)=x
13+0,2(4)=x
0,2(4)=y
10y=2,(4)
10y=2+0,(4)
0,(4)=z
10z=4,(4)
10z=4+0,(4)
10z=4+z
9z=4
z=4/9
10y = 2 + 4/9
10y = 22/9 |:10
y=22/90
0,2(4)=22/90
13 + 22/90=x
x=13 i 22/90
==================
5,3(2)=x
5+0,3(2)=x
0,3(2)=y
10y=3,(2)
10y=3+0,(2)
0,(2)=z
10z=2,(2)
10z=2+0,(2)
10z=2+z
9z=2
z = 2/9
10y = 3 + 2/9
10y=29/9 |:10
y= 29/90
5 + 29/90 = x
x= 5 i 29/90
=================
17,(5)=x
17 + 0,(5) = x
0,(5)=y
10y=5,(5)
10y=5 + 0,(5)
10y = 5 + y
9y = 5 |:9
y = 5/9
17 + 5/9 = x
x = 17 i 5/9
===============
1,2(6)=x
1,2(6) = 1 + 0,2(6)
0,2(6)=y
10y=2,(6)
10y=2+0,(6)
0,(6)=z
10z=6,(6)
10z=6+0,(6)
10z=6+z
9z=6 |:9
z = 6/9 = 2/3
10y = 2 + 2/3
10y = 8/3 |:10
y = 8/30
1 + 8/30 = x
x = 1 i 8/30
================
3,2(9)=x
3 + 0,2(9) = x
0,2(9) = y
10y = 2,(9)
10y = 2 + 0,(9)
0,(9)=z
10z=9,(9)
10z=9+0,(9)
10z=9+z
9z=9
z=1
10y = 2 + 1
10y = 3 |:10
y=3/10
3 + 3/10 = x
x = 3 i 3/10
Pozdrawiam :)
3,(15)= 3 i 15/99 = 3 i 5/33
11,(3)= 11 i 3/9 = 11 i 1/3
0,1(5)= 1,(5) : 10 = 1 i 5/9 * 1/10 == 14/9 * 1/10 = 14/90
-2,0(1)= -20,(1) : 10 = -20 i 1/9 * 1/10 = -181/9 * 1/10 = -181/90 = -2 i 1/90
-7,(8)= - 7 i 8/9
13,2(4)=132,(4) ; 10 = 132 i 4/9 * 1/10 = 1192/90 = 13 i 22/90
5,3(2)= 53,(2) : 10 = 53 i 2/9 * 1/10 = 479/90 = 5 i 29/90
17,(5) = 17 i 5/9
1,2(6)=12,(6) : 10 = 12 i 6/9 * 1/10 = 12 i 2/3 * 1/10 = 38/3 * 1/10 = 38/30 = 1 i 8/30
3,2(9)=32,(9) : 10 = 32 i 9/9 : 10 = 33 : 10 = 3,3