Question

Convert 11.42424242 … to a rational expression in the form of a over b, where b ≠ 0. i dont know how to convert 11.42424242 to a rational expression

Answer 1

What they are asking you to do is find the division problem that created this decimal.

Answer 2

no there asking to convert it into the form a over b

Answer 3

A over b is a division problem. :)

Answer 4

oh yh

Answer 5

The way to do this is to remove the repeating section.

Answer 6

how do you do that exactly?

Answer 7

This is done by setting the original number equal to x. In this case, x= 11.4242.... then multiply each side by 100 to get 100x=1142.4242. Then subtract x from each side. (x=11.4242). This will give you 99x=1130.9998. Divide each side by 99 to get x=1130.9998/99. Then simplify this to get the final fraction.

Answer 8

i am not following that solution

one thing to notice is that in \( 11.4242... \) , the \( .42 \) is periodic, which the whole thing you write as \( 11.\overset{—}{42} \) -- normally, if 42 was a natural number as a fraction you would write it \( \frac{42}{100} \) right? BUT since its periodic, you should always write it over \( n-1 \) so in our case \( 100-1 \)

thus, your answer would be \(11\frac{42}{99} \overset{\text{example: }\: 1\frac{2}{3}=\frac{1\cdot \:3+2}{3}}{\ \ \ \ =========\Rightarrow \ \ \ } \frac{1131}{99} \)

can we simplify that?

Answer 9

Your answer seems interesting. It does seem easier to do than the one I provide. However, in the end, they are almost the same with less than a 0.1 difference.

Answer 10

x=11.424242...
x=11+0.424242...
x=11+0.42+.0042+.000042+...
x=11+y
y=0.42+.0042+.000042+...
it is a geometric seris
a1=0.42
\[r=\frac{ 0.0042 }{ 0.42 }=\frac{ 0.0042 }{ 0.4200 }=\frac{ 1 }{ 100 }<1\]
\[y=\frac{ a }{1-r }=\frac{ 0.42 }{ 1-0.01 }=\frac{ 0.42 }{ 0.99}=\frac{ 42 }{ 99 }=\frac{ 14 }{ 33 }\]
\[x=11+\frac{ 14 }{ 33 }=\frac{ 363+14 }{ 33 }=\frac{ 377 }{ 33 }\]

Answer 11

second method
let x=11.424242...(1)
10x=114.24242...
100 x=1142.424242... (2)
(2)-(1) gives
99x=1131
\[x=\frac{ 1131 }{ 99 }=\frac{ 377 }{ 33 }\]