The three dots after the 777 indicate that the pattern repeats forever. Specifically the 7s go on forever (the 1 does not repeat and its only listed one time)
Let
x = 0.1777...
The goal is to find the value of x in terms of a fraction of whole numbers (eg like 2/3 or 4/5)
The trick is to somehow get the decimal portion that goes on forever to go away. We will do this through subtraction. But first, we need to do a bit of side work.
Multiply both sides of the equation above by 10
x = 0.1777...
10*x = 10*0.1777...
10x = 1.777...
Notice how this moves the decimal over 1 spot to the right
Then go back to the original equation for x and multiply both sides by 100
x = 0.1777...
100*x = 100*0.1777...
100x = 17.777...
Now the decimal is moved over two spots to the right
-----------------------------------
In summary so far, we have
10x = 1.777...
100x = 17.777...
If we subtract 100x - 10x then we'll have
100x - 10x = (17.777...) - (1.777...)
90x = 16
The decimal portion 777... cancels out when we subtract. This is because the terms line up perfectly and subtract to 0
The last few steps is to solve 90x = 16 for x. We divide both sides by 90 and then reduce as much as possible
90x = 16
90x/90 = 16/90
x = 16/90
x = 8/45
Therefore the final answer is the fraction 8/45
I recommend you use a calculator to confirm that 8/45 will have the decimal form of 0.1777...
Note: your calculator may round the last digit from 7 to an 8
3+2= degree 5.......sooooo yeshh
<span>75p/1pound = 75p/100p = 75/100 = 3/4
</span>
Answer:
slope: 1
/8
y-intercept: (
0
,
−
1
/4
)
To solve this problem, we have to make use of the standard
probability distribution tables for z test.
Since we are asked to find for the 72 percent level
confidence, then this means we are to look for the value of z which gives
(100-72)/2 = 14% on both sides of the tail.
So at 14% tail on one side, the z value is approximately:
1.08
Answer:
<span>± 1.08</span>