|Another Maths Lesson
||[Jan. 31st, 2007|04:16 pm]
Unofficial Murderous Maths Forum on LJ
Today we learnt about recurring decimals. Such as 0.444444... being 4/9 and so on. Me and Chunk were finding this easy, so he challenged me to find the equivalent fraction of 0.58666666... which at first I thought, is there such a fraction? Are there any decimal numbers which do not have an equivalent fraction? [Pi does spring to mind, but are there others?].
Following some thought I figured the answer would be 58/100 + 6.66/999 [which Chunk found was equal to 6/900]. Adding these gives 44/75. McMaffs then introduced such problems anyway with a different method:
let 0.5866666... = N
then 100N = 58.666666...
99N = 58.08
9900N = 5808
N = 5808/9900 = 44/75.
McMaffs then posed the problem 0.87444444....
Her solution was:
Let N = 0.8744444
then 100N = 87.444444
99N = 86.57
9900N = 8657
N = 8657/9900
Chunk then said "oh I have another method" and she let him go to the board to explain.
He said 0.874444 = 87/100 + whatever 0.004444444.... is.
He then said this was equal to 4/900.
McMaffs asked him to explain why.
He didn't know, neither do I, so this is my second question.
Chunk continues his working by adding the fractions and got:
783/900 + 4/900 = 787/900
At first McMaffs thought this was wrong until I pointed out it was equivalent to 8657/9900 [both numerator and denominator are 11 times smaller by the "Chunk theorem" method].
So yeah, this is the main point. Why is it 900? I assumed it would be like other recurring decimals [like 0.42424242... = 42/99] and feature denominators with all 9s, thats how I came up with 6.66/999 for the first problem in the first place. It did also occur to me that it was because it was like the normal ones [ie 4/9] but 100 times smaller, as its two decimal places to the right from where it should be, but I couldn't really explain it.
In other news, maths challenge tomorrow!