How do u turn this decimal into a fraction. 0. 7777.....?

Answer 1

I'll do an example that is a bit more instructive. Let's write
x=.23434343434...
as a fraction where the 3 and the 4 alternate.
Well, 10x=2.3434343434....
and 1000x=234.34343434...
Here, we multiplied by a power of 10 to get to the beginning of the repeating sequence and another power of 10 to get to the end.
Now substract the two:
990x=232,
so
x=232/990=116/495.

Your example is easier:
x=.7777777...
so
10x=7.77777....
Subtracting gives
9x=7, so x=7/9.

Answer 2

There is not much that can be done to figure out how to write 0. 7777 as a fraction, except to literally use what the decimal portion of your number, the . 7777, means.

Since there are 5 digits in 7777, the very last digit is the "100000th" decimal place.

So we can just say that . 7777 is the same as 7777/100000.

So your final answer is: 0. 7777 can be written as the fraction

Answer 3

If you are talking about 0.777... in decimal, then you can only approximate the value in base 10 as 7/9. In fact 0.777... is less than 7/9. However, if you were using base 9, you could write 0.7 (base 9) = 7/9 exactly.

The user Yeti gives you an example of how to find a fraction that is in essence the limit of the series: 7/10 + 7/100 + 7/1000 + ...

But be careful, this (7/9) is the limit, not the value of the above series. Do not listen to anyone who tells you that the sum of an infinite series is defined aas its limit. An infinite series cannot be summed (for obvious reasons). We can only find limits of infinite series (not actual values). When we find a limit, we are computing an upper bound for the series.

Thus 7/9 = 0.7 (base 9) and 7/9 is approx. = 0.777... (base 10)

Answer 4

0.777777..., which I will write as 0.'7', starts repeating right after the decimal point. The rule for such a decimal is that you put the repeating block of digits over a series of 9s with the same length:

7/9.

If it were 0.'142857', then you would put the 142857 over 999999:

142857/999999 = 1/7,

after reducing to lowest terms.

If the repeating starts later, then you re-express it so it shows a decimal repeating after the decimal point:

0.4166666... = 0.41'6' = 0.41 + (1/100)*0.'6' =

41/100 + (1/100)(6/9) =

41/100 + 2/300 =

123/300 + 2/300 = 125/300 = 5/12.

Answer 5

You don't. By your ...... you are indicating an unending, irrational number. Those do not convert to fractions without first modifying the number.

For example, .66666666....... is known to be 2/3. But it is always rounded up as something like .66666667 to truncate it. So, decided were you want to truncate and round up (or down if the string of unending numbers is a string of 5's or less). Then do as others have suggested, muliply the number by 1...any number times 1 is still the number, right?

The tricky part is the any number divided by itself, like 10/10, is 1. So you can take .77777778 X (1000000000/1000000000) = 77777778/1000000000, which is a fraction.

Answer 6

Converting a decimal into a fraction

Example

½ = 0.5

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The tenths positions starting at 0.1, 0.2, 0.3, 0.4 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0

The 0.5 decimal place is in the fifth position. since there are 10 positions the fraction becomes 5/10 or 1/2 after simplification.

When converting decimal to fraction consider the position of the decimal divided by 10.

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Click onthe URL below for additional information

www.webmath.com/dec2fract.html

Answer 7

numbers from 1-8 can be placed over 9 to get a repeating number.

(1/9) = .111111111
(2/9) = .222222222
(3/9) = .333333333
(4/9) = .444444444
(5/9) = .555555555
(6/9) = .666666666
(7/9) = .777777777
(8/9) = .888888888

Also some numbers that have 2 digits can be placed over 99 to get the repeating of that number

for ex: (11/99) = .1111111111 and (12/99) = .1212121212

Answer 8

7/9

Answer 9

7/9

Answer 10

it's 7/9