Question

Transforme as dizimas periódicas em frações geratrizes.


a) 0, 999...

b) 4,555...

c) 13,28444...

d) 174,16060...

e)3,271271...

f)0,73131...

g)18,453232...​

Me ajudem!!

Answer 1

a) 0, 999...

0,999...    x           . 10

9,999... = 10x

9,999... = 10x          -

0,999... = x          

------------------------------------

9,000 = 9x

x = 9/9

x = 1

1

b) 4,555...

4 + 5/9

36 + 5/9

41/9

c) 13,28444...

13 + (284 - 28)/900

13 + 256/900

13 + 64/225

225 . 13 + 64/225

2925 + 64 / 225

2989/225

d) 174,16060...

174 + (160 - 1)/990

174 + 159/990

174 + 53/330

330 . 174 + 53/330

57420 + 53/330

57473/330

e)3,271271...

3 + 271/999

999 . 3 + 271/999

2997 + 271 / 999

3268/999

f)0,73131...

731 - 7 / 990

724/990

362/495

g)18,453232...​

18 + (4532 - 45)/9900

18 + 4487/9900

9900 . 18 + 4487/9900

178200 + 4487/9900

182687/9900