Question

Transforme as dízimas periódicas e os decimais em frações a)2,1444... b)0,5. c)6,21444... d)0,23. e)0,681. e)3,42777... f)1,333...

Answer 1

a) $2,1444...=2+0,1444...=2+ \frac{14-1}{90}=2+ \frac{13}{90}= \frac{193}{90}$

b) $0,5= \frac{5}{10}$

c) $6,21444...=6+0,21444...=6+ \frac{214-21}{900}=6+ \frac{193}{900}= \frac{5593}{900}$

d) $0,23= \frac{23}{100}$

e) $0,681= \frac{681}{1000}$

e) $3,42777...=3+0,42777...=3+ \frac{427-42}{900}=3+ \frac{385}{900}= \frac{3085}{900}$

f) $1,333...=1+0,333...=1+ \frac{3}{9}= \frac{12}{9}= \frac{4}{3}$