answersLogoWhite

0


Best Answer

This is made quite easy with the following observations:

5/9 = 0.5555...

7/9 = 0.7777...

12/99 = 0.121212...

23/99 = 0.232323...

456/999 = 0.456456456...

78/999 = 078/999 = 0.078078078...

So we can see that fractions with a denominator of 9, 99, 999, 9999, ... are pretty useful for making repeating decimals. All we have to do is to reduce the fraction to its lowest terms. For example, let's take the repeating decimal 0.027027027...

Clearly this is 27/999 = 1/37 (having divided top and bottom of the fraction by 27)

Now let's try something more tricky. Take a look at 0.4588888888...

This isn't simply something divided by 99.. since the 45 bit doesn't repeat. What we need to do is move the decimal point over to the start of the repeating bit. In this case we multiply by 100 to get 45.888888...

Now we know the fraction part is 8/9. In total we have 45 + 8/9 = 413/9 (changing into a top-heavy fraction will make things easier for us).

So 45.88888... = 413/9

Now just divide both sides by 100 to get:

0.458888... = 413/900

User Avatar

Wiki User

13y ago
This answer is:
User Avatar
More answers
User Avatar

Wiki User

13y ago

The pattern is divide the repeating number by the amount of nines equivalent tot he amount of digits in the repeating pattern. For example: 0.44444... = 4/9 and .123123123123... = 123/999.

This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: How do you change a repeating decimal into a fraction?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

How do you change repeating decimal to fraction?

you don't it just keeps recurring


What is the fraction of the repeating decimal 0.7...?

The fraction of the repeating decimal 0.7... is 7/9


How can a repeating decimal turn into fraction?

decimal and repeating bar


Is the fraction 13 a terminating or repeating decimal?

It is a repeating decimal.


How do you convert 0.2 a repeating decimal into a fraction?

0.2 a repeating decimal into a fraction = 2/9


How do you write the repeating decimal 1.1 as a fraction?

repeating decimal 1.1 as a fraction = 10/9


How can a decimal change to a repeating fraction?

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


How do you determine whether you can write a given decimal as a fraction?

If the decimal is terminating or repeating then it can be written as a fraction. Decimal representations which are non-terminating and non-repeating cannot be expressed as a fraction.


How can a decimal greater than 1 be a repeating decimal?

A decimal number is like a mixed fraction: it has an integer part and a fractional part. If the fractional part is a repeating fraction then the whole number is represented by a repeating decimal.


Can every rational fraction be written as a repeating decimal?

Any rational number is either a repeating decimal, or a terminating decimal.


What is 2.78 repeating?

It is a fraction in decimal form.


How do you change terminating but reapeating decimal into a fraction Example 0.88888?

It is not possible to have a terminating decimal which repeats or a repeating decimal which terminates. The two types are mutually exclusive.