Answer:
-0.9090... can be written as
.
Explanation:
Any <em>repeating </em>decimal can be written as a fraction by dividing the section of the pattern to be repeated <em>by </em>9's.
We can start by listing out
0.909090... = 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
Now. we let this series be equal to x, that is
= 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
Now, we'll multiply both sides by 100
.
= 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + ...
Then, subtract the 1st equation from the second like so:
= 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
= - 9/10 - 0/100 - 9/1000 - 0/10000 - 9/100000 - 0/1000000 - ...
And we end up with this:

Finally, we divide both sides by 99 in order to isolate x and get the fraction we're looking for.

Which can be reduced and simplified to

Hope this helps!
1/2 + 1/3 = (3*1)+(2*1) / (2*3) = (3+2)/6 = 5/6
tinha 5/6 de litro
para 1 litro faltam 4/6 de litro
para 3 litros faltam 2 litros e 4/6 de litro ou, simplificando:
4/6 = 2/3, logo, faltam 2 litros e 2/3 de litro.
Answer:
68 plants.
Step-by-step explanation:
Let x represent the number of plants that Reuben bought from the nursery.
We have been given that Reuben bought a whole bunch of plants at the nursery the other day. Right away, five died. So number of plant left would be
.
We are also told that then our dog dug up 2/9 of them. So number of plants left after dug-up would be
.
Further a rabbit came and ate ½ of what was left. So number of plants left would be
.
Since Reuben had only 7 plants left, so we will equate our expression with 7 and solve for x as:





Therefore, Reuben bought 68 plants at the nursery.