how do you make a repeating decimal into a fraction if you dont no what after it?

Answer 1

When you have a repeating decimal, say 0.181818... take the repeating digits (18) and put them over an equivalent number of nines (99).

So 0.181818... = 18/99
You can reduce this to 2/11

Double-check with your calculator.

Here are some other examples:
0.532532532...

= 532/999
= 42/111

Or:
0.333333....
= 3/9
= 1/3

Note: it gets tricker if you have part of the decimal that doesn't repeat... say 0.16666....

x = 0.166666....

Notice how if you multiply by 10, you'll get that non-repeating part before the decimal.

10x = 1.66666....

Using the method above, we know that 0.66666... = 6/9 = 2/3

And we add one to this:
10x = 1 + 2/3

Make it a mixed fraction:
10x = 5/3

Now divide the 10 from both sides:
x = 5/30

Reduce:
x = 1/6

So 0.166666... = 1/6

Double-check with the calculator to confirm.

Answer 2

I don't think there is any really easy to way to do this.

Theres some obvious ones that jump out at you like
0.111111... = 1/9
0.222222... = 2/9
0.333333... = 3/9

you can repeat this idea with repeating decimals
say we had
0.43434343.... you put the repeating number over 99
so 43/99 would be the number above
you can do the same with 999, or 9999
like.. 0.567567567... = 567 / 999


hope this helps!

Answer 3

I love this question.
OK...
Let's use 5.6 repeating.

Let x = 5.6 repeating.
Then 10x = 56.6 repeating, right? (if I multiply both sides by 10)

Now you set up a system of equations and subtract.
I can't underline so imagine there's a long line underneath these next two equations.
10x = 56.6rep
1x = 5.6rep

Now subtract on the left side and subtract on the right side.
9x = 51 (because the .6 repeating part subtracts out! Yay!)

Divide both sides by 9
So...
x = 51/9 or
5 and 6/9 or
5 and 2/3

Want a different one? :)

Answer 4

example: n = 0.6333...
since there is one digit repeating (the 3)
multiply by 10
10n = 6.3333...
n = 0.633333...
subtract and get
9n = 5.7 divide by 9
get n = 5.7/9 == 57/90 == 19/30 is the fraction
check by doing 19divided by30 on calculator...

example: n = 0.2454545...
since there are two digits repeating (45)
multiply by 100
100n = 24.545454...
n = 0.245454...
subtract
99n = 24.3
divide
n = 24.3/99 == 243/990 == 27/110
~~

Answer 5

Puzzling has pretty much got the right answer, but didn't show all the steps.


Suppose you have the number
d = 0.1818181818...
Multiply by 100 to get
100 * d = 18.18181818 . . .
Subtract the two equations.
You get
99 * d = 18.181818. . . - 0.18181818. . .
99 * d = 18
So,
d = 18 / 99

Answer 6

if its tenths reapeting such as 3.3333333 then its 3 1/3

6.666666666666 6 2/3

Answer 7

we have diffrnt ways of doing those such things. better to study ur lesson well!

tke care!

Answer 8

taylor series