Question

Need help, will give medals. Represent 1.03(3 is repeating) as a fraction. Use geometric series

Answer 1

31/30

Answer 2

how did you do that though

Answer 3

i know the answer but i need to know how to do it

Answer 4

kk.. let 1.03333=x
therefore 10.333333333=10x
Hence 9x= 9.300
Therefore x=9.3/9
x= 31/30

Answer 5

Is that ok?

Answer 6

no i need it to be represented in geometric series

Answer 7

geometric series?

Answer 8

Ok so we have 1.033333... and that is equal to 1 + 0.3 + 0.003 + 0.0003 + ...

We leave the 1 for now and focus on the other numbers.
What is the first term in our geometric series? What is the common ratio? If you remember your geometric series sum to infinity, you should be able to complete the question.

Answer 9

Oops, I meant 1 + 0.03 + 0.003 etc (I forgot an extra 0 in the first term of the series)

Answer 10

So the sum of a geometric series is S = a/(1-r), where S is the sum to infinity, a is the first term and r is the common ratio.

If our series was 1/2 + 1/4 + 1/8 + ... then our first term is 1/2, our common ratio is 1/4 divided by 1/2 = 1/2, so a = 1/2 and r = 1/2. So then we would have 0.5/(1-0.5) = 1, so our sum to infinity would be 1 in that scenario.

Using a similar method, you could work out the sum to infinity of the series in your situation. Just remember to add 1 again at the end :)

Answer 11

In case you were confused about how to get the common ratio, it's Tn divided by Tn-1, or in other words, any term in the series divided by the term before it.

Answer 12

Omg ... i had no idea!!!-- lol my basic maths sorry for wasting ur time...

Answer 13

So, to give you a start, 0.03 is the first term in our geometric series. 1 isn't, we're excluding it because it doesn't fit the rest of the series. So our final answer will be 1 + some geometric series where the first term is 0.03, the second term is 0.003 and so on.

From what I said previously, what would r (our common ratio) be? Using these numbers are the sum to infinity formula, you can quite easily calculate the final answer.

Answer 14

and the sum to infinity formula* -- sorry, typos everywhere