repeating decimals to fractions

[rebecca12345]

Decimals to Fractions HELP?
Hi,
I'am doing terminating decimals to fractions,
----
the question is 3.78
(the --- is representing the repeating decimal)
anyway someone wrote on here that all you have to do is put the number = 78 over that many 9's to get you're answer 78/99= 3 29/33
this way worked for the other problems but not this one.
how do they figure out the answer 3 29/33?
Could you tell me step By step

 

[mmm4444bot]

I'am doing terminating decimals

---
3.78

Are you talking about the number 3.78787878… ?

This number is not a terminating decimal. It is a repeating decimal. The pattern 78 repeats forever.

All terminating decimals eventually display this pattern at the end: 00000000…

someone wrote on here that all you have to do is put the number 78 over that many 9's

They are wrong. Doing that only gives you the repeating part 0.78787878…

how do they figure out the answer 3 29/33 ?

That's the wrong answer for 3.78787878…

3.78787878… is the decimal form of the rational number 125/33

The rational number 125/33 equals the mixed number 3 26/33

The mixed number 3 26/33 means 3 + 26/33

And this is the same as 3 + 78/99



3.87878787… is the decimal form of the rational number 128/33

The rational number 128/33 equals the mixed number 3 29/33

The mixed number 3 29/33 means 3 + 29/33

And this is the same as 3 + 87/99



I'm not exactly sure what you were trying to do, but have you got it figured out now ?

 

[junicate]

rebecca, you have the right idea about using 9's to convert a repeating decimal to a fraction. the rule is to express the repeating part over as many 9's as there are digits in the repeating part. so if you want to express 3.7878... as a fraction, you make it 3 + 78/99, which reduces to 3 + 26/33.

Another example, if you want to convert 2.3444... (just the 4's repeat), you write it as 2 + 3/10 + (1/10)(4/9), and then simplify it from there. Since the repeating part is moved over one decimal place, you have to mulitply it by 1/10.

you can also use a repeating decimal calculator http://www.had2know.com/academics/conve ... lator.html