Question

Transformati in fracti ordinare: a)5 ,(1) , b) 0,7(3) c) 0, (15) d) 0,72) e) 0,(027), f) 65,65(65) , g) 2,01(351)

Answer 1

a) 5,(1) = 5 intregi 1/9 = ( 5·9 + 1) / 9 = 46 / 9
b) 0,7(3) = ( 73 - 7) / 90 = 66/ 90 = 22 / 30 = 11/ 15
c) 0,( 15) = 15/ 99 = 5/ 33
d) 0, 72 = 72/ 100 = 36/ 50 = 18/ 25
e) 0,( 027) = 27/ 999 = 3/ 111
f) 65,65(65) = ( 656565 - 6565) / 9900 = 650000 / 9900 = 6500 / 99
g) 2,01(351) = ( 201351 - 201) /99900 = 201150 / 99900 = 20115 / 9990 =
     = 4023 / 1998 = 1341 / 666 = 447 / 222 = 149 / 74

Answer 2

a) 5,(1) = 5 $\frac{1}{9}$ = $\frac{46}{9}$

b)  0,7(3) = $\frac{73 - 7}{90}$ = $\frac{66}{90}$ = $\frac{11}{15}$

c)  0,(15) = $\frac{15}{99}$ = $\frac{5}{33}$

d) 0,72 = $\frac{72}{100}$ = $\frac{18}{25}$

e)  0,(027) = $\frac{27}{999}$= $\frac{3}{111}$

f)  65,65(65) = 65 $\frac{6565 - 65}{9900}$ = 65 $\frac{6500}{9900}$ = 65 $\frac{65}{99}$ = $\frac{6500}{99}$

sau:
65,65(65) = $\frac{656565 - 6565}{9900}$ = [tex] \frac{650000}{9900} [/tex] = $\frac{6500}{99}$

g)  2,01(351) = 2 $\frac{1351 - 1}{99900}$ = 2 [tex] \frac{1350}{99900} [/tex] = $\frac{201150}{99900}$ = $\frac{4023}{1998}$ = $\frac{149}{74}$