if a decimal looks like 15.312121212121212
what is the rational form, show your work
2007-01-16 05:57:09 · 6 answers · asked by Zidane 3 in Science & Mathematics ➔ Mathematics
Assuming the "121212..." part goes on forever, it is a rational number. So it's already in "rational form". You could write it as "15.312" with a bar drawn above the "12" to show that's the part that is repeating.
Maybe they meant "write it as a fraction were both the numerator and denominator are whole numbers"? In that case, here's the trick. Let N = the number:
N = 15.3121212...
100N = 1531.2121...
100N - N = (1531.212121...) - (15.312121...)
99 N = 1515.9 [notice that the "212121..." part cancels out]
990N = 15159
N = 15159/990
I don't know why some other people are suggesting the answer is just "15.312". That's just rounding off the number. 15.312 is less than (and thus not equal to) 15.31212121212...
2007-01-16 06:33:37 · answer #1 · answered by Anonymous · 1⤊ 0⤋
the repeating part is .012121212121212...
Multiply by 10
0.121212121212
which is our X (in rational numbers)
This gives us a repeating fraction beginning right after the point, with a "period" of 2 digits. Since we use base 10, a two-digit period corresponds to 100
Multiply by 100
100 X = 12.12121212121212
Subtract 100X -X = 99X
12.121212121212 - 0.121212121212 = 12
99X = 12
X = 0.1212121212... = 12/99
Because we multiplied by 10 at the start, we have to divide by 10 to get 0.01212121212... = 12/990
15.31212121212 = 15.3 + 12/990
15 + 3/10 +12/990
3/10 + 12/990 = 297/990 + 12/990 = 309/990
you can simplify the fraction
309/990 = 103/330
15 + 103/330 = 15.31212121212...
(103 is prime, and 330 is not divisible by 103)
PS
geezerbill's is better.
Using his format, my answer becomes:
15 + 103/330 = 4950/330 + 103/330
5053/330
2007-01-16 14:33:39 · answer #2 · answered by Raymond 7 · 0⤊ 0⤋
I'm pretty sure that rational form is when the number can be made into a fraction and irrational form is when it cannot. So, since the 15.31212 continues, the rational form would just be 15.312.
2007-01-16 14:24:11 · answer #3 · answered by b 5 · 0⤊ 1⤋
My teacher taught me that. since the numbers after 15.312 are repetative, we'll just take 15.312. Then after you write 15 312
___
1000
2007-01-16 14:03:53 · answer #4 · answered by Anonymous · 0⤊ 1⤋
try doing your own homework and maybe you'll learn something
2007-01-16 14:50:30 · answer #5 · answered by bush deathgrip 2 · 0⤊ 0⤋
15.3+0.01212......
15.3+12/990
now, you just add up and leave it as fraction, i dont have my calculator now. Sorry!!
2007-01-16 14:02:19 · answer #6 · answered by 7 · 0⤊ 1⤋