Best Answer

Notice the pattern. One digit repeated is always that number over 9. Two digits repeated is always those two digits over 99 and so on.

0.7777 repeated = 7/9

0.5454 repeated = 54/99

0.125 repeated = 125/999

User Avatar

Wiki User

7y ago
This answer is:
User Avatar
More answers
User Avatar

Wiki User

8y ago

Here is an example. Convert 0.848484... into a fraction.Call this number "x". Write two equations:

100x = 84.848484...

x = 0.848484...

(Note: the factor 100 is used because 2 digits are repeated. For 1 digit, use the factor 10; for 2 digits use the number 100; for 3 digits use the number 1000; etc.)

Subtract the second equation from the first.

99x = 84

If you solve for "x", you get your original number (which we called "x") as a fraction. In this case, x = 84/99. Simplify the final result, if possible.

This answer is:
User Avatar

User Avatar

Wiki User

7y ago

Until you become expert at this I suggest you do this in two stages. Suppose there are c digits after the decimal place where the digits are non-repeating, and then you get a string of d digits which repeat. Then the numerator is the original string, without the decimal point, and including one lot of the repeated digits minus the original string with none of the repeating digits. The denominator is 10^c*(10^d - 1), which is a string of d 9s followed by c 0s.
For example 123.26159159… There are 2 digits, "26", after the decimal point before the repeats kick in so c = 2, and the repeating string "159" is 3 digits long do d = 3. So the numerator is 12326159 – 123216 = 12313833 and the denominator is three 9s followed by two 0s = 99900 Therefore the fraction is 12313833/99900. You should then check to see if the fraction can be simplified.

This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: How to turn repeating decimals into fractions?
Write your answer...
Still have questions?
magnify glass
Related questions

Why are repeating decimals changed to fractions?

There are times when working with fractions is more convenient than working with decimals.

Is 0.16 repeating irrational?

No, no repeating decimal is irrational. All repeating decimals can be converted to fractions. They are, however, non-terminating.

How do you add repeating decimals?

Convert the repeating decimals into fractions, and then add those. If you need it as a decimal, then you can just convert the product back into a decimal!:)

Real life situation for changing repeating decimals into fractions?

there are None!

What can rational numbers be expressed as?

fractions or decimals

What is the relationship between repeating decimals and fractions?

They are both representations of rational numbers.

Why are repeating decimals common to get after dividing?

all rational fractions are repeating. When you divide, eventually the remainder will repeat and then will the sequence

Is a repeating decimal rational?

yes, repeating decimals (those that have infinite - never ending - number of digits after the decimal point and these decimals show repeating pattern) are rational numbers, because they can be written as fractions.

How do you turn decimals into ratios?

Convert them to fractions.

Is 3.25 repeating an integer?

No because integers are whole numbers without decimals or fractions.

How can a decimal change to a repeating fraction?

Fractions don't repeat, decimals do. 4/9 = 4 divided by 9 = 0.4444 repeating

What is it called when fractions terminating repeating decimals integers and percents called?

They are called rational numbers