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## Topic review (newest first)

Jenilia
2006-03-26 17:20:25

Yes

RickyOswaldIOW
2006-03-25 16:19:11

I'm 19 and studying a-level mathematics.  You're 12 you say?

George,Y
2006-03-24 02:09:05

By the way, is SAT that HaaaaarD?

George,Y
2006-03-24 02:07:34

Yeah, as Mr Hollis put in his Caculus book, we are using sum of infinite series IMPLICITLY.

Numbers are a theory, "theory" means approximation

0.99... is accurate to leave perhaps only one particle uncollected from recursively cutting a cake into equally 10 pieces, then collecting 9 and leaving the other one to be next round cut-ee.

ganesh
2006-03-23 21:56:52

How else can 0.9999......recurring indefinitely be expressed as a fraction?
It may appear inaccurate, but think of it, you may never encounter the number 0.999999......... in any area of mathematics!

Jenilia
2006-03-23 21:53:01

But then it ist accurate right?

ganesh
2006-03-23 21:24:35

All recurring decimals, that is decimal numbers where numbers are repeated without ending after the decimal, can be converted into fractions.
For example, 0.21212121..... can be coverted into a fraction this way.
Let x = 0.212121....
100x = 21.212121....
Finding the difference of the two,
99x=21, therefore, x=21/99 or 7/33.

When we try to convert 0.99999.. this way, this is what happens:-
Let x = 0.99999999....
10x = 9.99999999....
Finding the difference of the two,
9x=9 or x=1.
Yes, 0.999999......... cannot be expressed as a fraction and can only be written as 1!

ganesh
2006-03-23 21:17:32

Jenilia,
To find the sum of 1/5 + 1/50 + 1/500 + 1/5000...,
rewrite it as 1/5(1+1/10+1/100+1/1000....)
The series of numbers inside the bracket forms a Geometric Progression. The sum would be 1/(1-1/10)=1/(9/10)=10/9.
Therefore, the sum 1/5 + 1/50 + 1/500 + 1/5000... = 1/5(10/9)=2/9=0.2222......

This is the answer you got!

Jenilia
2006-03-23 20:39:44

Another problem:
Find the fraction in its simplest form of 1/5 + 1/50 + 1/500 + 1/5000...
I do know how to work this out if it is correct,
I can simplify it as 0.2+0.02+0.002...=0.2222...
I'm using Algebra,
Let x be 0.222...
10x=2.222
9x (10x-x)=2
x=2/9
Now, If I have a No. like 0.999999...,is there anyway to simplify it?

Jenilia
2006-03-19 23:08:13

Thank you sooo much ganesh!

ganesh
2006-03-18 17:33:02

Q 30:-
Team D wins against A and B, draws with C and has a total of 7 points.
Team C wins against B, draws with D and A, and has a total of 5 points.
Team B wins against A, losses to both D and C, and has a total of 3 points.
Team A draws with C, losses to D and B, and has a total of 1 points.

Points Tally:-

Team        Played        Won             Lost        Drawn          Points
D                3              2                  0               1                 7
C                3              1                  0               2                 5
B                3              1                  2                0                3
A                3              0                  2                1                1

ganesh
2006-03-18 17:18:22

Jenilia,
I shall try Q22 first.
The question is to find the total of the first 100 numbers of the series.
1 to 9 is 9 numbers. It can be seen that thereafter, 10, 11, 12 etc have been given as two separate digits.
10 to 99 would be 2 digits each, therefore, 180 numbers.
But we require only 99 more of these.
Hence, 10 to 54 is 45 numbers and the 5 in 55 is to be taken.
1 occurs 16 times, 2 occurs 16 times, 3 occurs 16 times, 4 occurs 16 times, 5 occurs 11 times, 6, 7, 8, and 9 occur 5 times each.
Therefore, the total would be
16(1+2+3+4) + 11(5)+5(6+7+8+9)
=16(10) + 55 + 5(30) = 160 + 55 + 150 = 365.

Jenilia
2006-03-18 13:51:33

Q30,  Four football teams A,B,C and D are in the same group. Each team plays 3 matches, one with each of the other 3 teams. The winner of each match scores 3 points; the loser scores 0 points; and if a match is a draw, each team scores 1 point. After all the matches, the results are as follows:
(1)  The total score of 3 matches for the 4 teams are consecutive    odd  numbers.
(2)  D has the highest total score.
(3)  A has exactly 2 draws, one of which the match with C.
Find the total score for each team.

Jenilia
2006-03-18 13:43:05

It looks like I have another problem here. It is taken from the Singapore Mathematical Olympiad 2002.
Q22,  Find the sum of the first 100 No. in the following sequence.
1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,2,0,...

Jenilia
2006-03-17 23:53:20

Thanks so much for helping me. I definitely understand better now!