Question

Write the repeating decimal, 0.150150 . . . , as the ratio of two integers in lowest terms.

Answer 1

these are the choices
A) 125/1000
B) 150/1000
C) 150/999
D) 50/999
E) 50/333

Answer 2

\[\begin{align} 0.150150\dots&=\frac{150}{1000}+\frac{150}{1,000,000}+\frac{150}{1,000,000,000}+\ldots\\
&=\frac{150}{1000}\left( 1+\frac{1}{1000}+\frac{1}{1,000,000}+\dots\right)\\
&=\frac{150}{1000}\sum_{i=0}^{\infty}\left(\frac{1}{1000}\right)^i \,\,\,\,\,\,\,\,\text{geometric series }\\
&=\frac{150}{1000}\frac{1}{1-\frac{1}{1000}}\end{align}\]

Answer 3

The rest should be simple simplification. And just be sure your answer is in the lowest terms, as mentioned in the instructions!

Answer 4

this was really helpful, I wrote down the steps myself to practice how to solve it
thank you so much @kirbykirby

Answer 5

:) awesome

Answer 6

thanks :)

Answer 7

np