# Thread: Change repeating decimal to fraction

1. ## Change repeating decimal to fraction

0.143 (3 repeating) I solved the following way:
x=0.143 (3 repeating)
100x=14.3 (3 repeating)
1000x= 143.3 (3 repeting)
1000x - 100x = 143.3-14.3
900x = 129
x= 129/900

My question: how to solve this problem using geometric series?
14/100 + 0.003 (3 repeating)

I guess we need to find fraction for 0.003 (3 reapeting)

What is the first term? What is the common ratio?

Thanks

2. You've got the $\frac{14}{100}$ just fine.

Then you're adding in .003 + .0003 + .00003 + .000003 + ...,

so your first term is .003, and your common ratio is $\frac{1}{10}$.

Also, it's possible to say that .1433333333... is .333333333... -.2+.01, or $\frac{1}{3} - \frac{1}{5} + \frac{1}{100}$.

3. Thank you, got it

4. ## Simplify

Henderson, I see you are online now. Can you please tell me whether 8 taken 7 at a time is 56 (it's on binomial theorem) It was not explained in class, but is included in the test review, I do not know what it is about, just used the formula.

Thank you

5. Sure-

8 taken 7 at a time is the same as the number of ways to leave one guy out, so there are only going to be 8 ways to do this.

Here's a decent explanation of what you're talking about: Binomial Theorem.

Hope this helps!

6. ## Use Pascal's Triangle and expand

(2x-3)^4 = 16x^4-96x^3+216x^2-216x + 81

Is this correct? I did it using binomial theorem, why do I need to use Pascal's triangle?

Thank you

7. Looks correct to me.

You know the numbers you're getting from combinations that you're multiplying into each term (in your example, the 1,4,6,4, and 1)? Rather than run a combination for each term, Pascal's triangle gives you the whole list of coefficients (since you raised to the fourth power, these numbers are the fourth row of Pascal)