Question

Encontre a fração geratriz das dizímas a seguir
a)-2,444
b)0,111
c)17,888
d)-6,3535
e)0,292929
f)2,102102102

Answer 1

Resposta:

Explicação passo-a-passo:

a)  -2,444... = - 2 + 4\9 = -  2.9+4\9 = - 22\9

b)  0,111... = 1\9

c)  17,888... = 17 + 8\9 =

17.9+8\9 = 161\9

d)  -6,3535... = -  6 + 35\99 =

-  6.99+35\99 = - 629\99

e)  0,2929... = 29\99

f)  2,102102... = 2 + 102\999  =

2.999+102\999 = 2100\999 = 700\333

Answer 2

Oie, Td Bom?!

a)

$≈ - 2,444...$

$= - 2 \frac{444}{999}$

$= - \frac{2 \: . \: 999 + 444}{999}$

$= - \frac{1998 + 444}{999}$

$= - \frac{2442}{999}$

$= - \frac{2442 \div 111}{999 \div 111}$

$= - \frac{29}{9}$

b)

$≈0,111...$

$= 0 \frac{111}{999}$

$= \frac{0 \: . \: 999 + 111}{999}$

$= \frac{0 + 111}{999}$

$= \frac{111}{999}$

$= \frac{111 \div 111}{999 \div 111}$

$= \frac{1}{9}$

c)

$≈17,888...$

$= 17 \frac{888}{999}$

$= \frac{17 \: . \: 999 + 888}{999}$

$= \frac{16983 + 888}{999}$

$= \frac{17871}{999}$

$= \frac{17871 \div 111}{999 \div 111}$

$= \frac{161}{9}$

d)

$≈ - 6,3535...$

$= - 6\frac{3535}{9999}$

$= - \frac{6 \: . \: 9999 + 3535}{9999}$

$= - \frac{59994 + 3535}{9999}$

$= - \frac{63529}{9999}$

$= - \frac{63529 \div 101}{9999 \div 101}$

$= - \frac{629}{99}$

e)

$≈0,292929...$

$= 0 \frac{292929}{999999}$

$= \frac{0 \: . \:999999 + 292929 }{999999}$

$= \frac{0 + 292929}{999999}$

$= \frac{292929}{999999}$

$= \frac{292929 \div 10101}{999999 \div 10101}$

$= \frac{29}{99}$

f)

$≈2,102102102...$

$= 2 \frac{102102102}{999999999}$

$= \frac{2 \: . \: 999999999 + 102102102}{999999999}$

$= \frac{1999999998 + 102102102}{999999999}$

$= \frac{2102102100}{999999999}$

$= \frac{2102102100 \div 3003003}{999999999 \div 3003003}$

$= \frac{700}{333}$

Att. Makaveli1996