## debrasha 2 years ago Write the fractional equivalent (in reduced form) to each number. 0.3 repeating 0.125 0.16 repeating 0.1 0.6 repeating 0.2 0.75 Please Help!!!!

1. debrasha

@Agent_Sniffles @d92292 @Kathatesmath94 @SamuelAlden917 @LonelyandForgotten @LoveYou*69 @Gabylovesyou

2. debrasha

3. debrasha

I really need help!

4. jagatuba

This is quite simple when you know how to convert a decimal to a fraction. Just remember that anything to the right of the decimal is in increments of 1/10. IE: 0.1 = 1/10 0.01 = 1/100 0.001 = 1/1000 and so on. So most of these are pretty straight forward. I don't want to answer your questions for you because I know that you are capable of answering them after a little coaxing, but I will give you a couple examples that you can apply. 0.140 = 140/1000 = 7/50 0.6 = 6/10 = 3/5

5. debrasha

@FirstFrostByte @jishan @kaylynn_013 @tacamry @darkside3704

6. debrasha

Jagatuba please give me the answers to these ones. I still dont understand it.

7. debrasha

If u help me and give me the answers to just these Ill give u a medal..

8. debrasha

9. jagatuba

I cannot give you the answers, but I can break down the examples a bit more for you: 0.140 is really 0.14 because the 0 is meaning less (that was my bad). So 0.14 is 14/100 because the second digit to the right of the decimal is the 1/100 column. 14/100 can be reduced to 7/50 by dividing the top and bottom of the fraction by 2. 0.6 is 6/10 since the number is only one digit to the right of the decimal which is the 1/10 column. You can reduce 6/10 to 3/5 also by dividing top and bottom by 2. Does that make more sense?

10. debrasha

ig but I still dont know the answers....

11. jagatuba

Well lets figure out one of them together then. Let's try, 0.125. what column is the last digit (5) in?

12. debrasha

(5) is in the thousandths place

13. jagatuba

Right so represented fractionally it is 125 x 1/1000 or 125/1000. Now reduce.

14. debrasha

1/8

15. jagatuba

Yes! It really is as simple as that. Repeating decimals are a bit different, but do the regular ones first.

16. debrasha

So then on 0.1 wouldnt the answer be 1/10

17. jagatuba

Correct.

18. debrasha

so then on 0.2 wouldnt the answer be 1/5

19. jagatuba

Unless the 1 is repeating. if it is repeating then it is 1/9.

20. jagatuba

Yes 0.2 = 2/10 = 1/5

21. debrasha

0.75 How would I do this one?

22. jagatuba

Okay. what column is the 5 in?

23. debrasha

hundredths

24. jagatuba

Right. So how many 1/100's do you have? Can you write it in fraction form?

25. debrasha

wouldnt it be 75/100

26. jagatuba

Yes. Now reduce.

27. debrasha

3/4

28. jagatuba

Yes!

29. debrasha

0.3 repeating I need help.

30. jagatuba

Okay. I have to think about the easiest way to explain this, so give me a minute to gestate something. Okay?

31. debrasha

ok.

32. jagatuba

Alright. let's see if you can follow me on this. The fractions that we have been dealing with so far are rational numbers. When decimals repeat they are irrational so cannot readily be represented as a fraction. For example 0.3 repeating cannot be 3/10 because there is another 3. It can't be 33/100 because there is another 3. It cannot be 333/1000 because there is another 3 and so on. It's not rational. So suppose that you have a repeating decimal, and it looks like .(a)(a)(a)... where (a) is some sequence of repeating digits (technically, (a) is called the "repetend," i.e., "the thing which is repeated"). For instance, for 1/9 = .111111..., (a) is 1 for 1/11 = .09090909..., (a) is 09 for 1/7 = .142857142857..., (a) is 142857 So you follow me so far?

33. debrasha

I dont get it. 0.16 repeating help me on this one so i can see if i know how to do it?

34. debrasha

???

35. debrasha

nvm I already summited the assignment.Thanks though.

36. jagatuba

Well don't get ahead of me here. I want to be sure you understand what I'm about to explain. We'll get to 0.16 in a second. I want to be sure you know how to get the repetend. Now, First, you have to count the number of digits in the repetend. When (a) is 3, the number of digits is 1, when (a) is 09, the number of digits is 2, and when (a) is 142857, the number of digits is 6. Now, multiply your repeating decimal by a power of 10, namely, the power of 10 which is a 1 followed by a number of zeros equal to the number of digits in the repetend. That's a mouthful, so let's see how it works in the examples above: For 0.33333..., the repetend is 3, and that has *one* digit, so multiply by a 1 followed by *one* zero, i.e., by 10 For 0.090909..., the repetend is 09, which has *two* digits, so multiply by a 1 followed by *two* zeros, i.e., by 100 For 0.142857142857..., the repetend is 142857, which has *six* digits, so multiply by a 1 followed by *six* zeros, i.e., by 1,000,000 (one million). If we multiply the repeating decimal by a power of 10 in this way, we end up with a decimal which has the repetend to the LEFT of the decimal point, and the same repeating decimal we started out with to the RIGHT of the decimal point: Multipy 0.33333... by 10, and we get 3.33333... Multiply 0.090909... by 100, and we get 9.090909... Multiply 0.142857142857... by 1000000, and we get 142857.142857... Still following me?

37. debrasha

What online school do u do?

38. jagatuba

Sorry, just saw your reply (it scrolled of the screen. Do you still want to know how to do this?

39. debrasha

no its okay. thanks so much for all ur help. I appreciate it...

40. jagatuba

No problem