Home » Blog » Express the given decimal number as a quotient of two integers Express the given decimal number as a quotient of two integers by RoRi February 29, 2016 Let Express as an infinite series, find the sum, and express as a quotient of two integers. We have Related
![\[ x = 0.4444\ldots. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-cedcc8404bbae6789b82cf1b3d2eda51_l3.png "Rendered by QuickLaTeX.com")
as an infinite series, find the sum, and express as a quotient of two integers.![\begin{align*} x = 0.4444\ldots && \implies && x &= 0 + \sum_{k=1}^{\infty} \frac{4}{10^k} \\[9pt] &&&&&= -4 + 4 \sum_{k=0}^{\infty} \frac{1}{10^k} \\[9pt] &&&&&= -4 + 4 \left( \frac{1}{1 - \frac{1}{10}} \right) \\[9pt] &&&&&= \frac{4}{9}. \end{align*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-1a4bc476f526bacceebbce1b668a667d_l3.png "Rendered by QuickLaTeX.com")
as an infinite series, find the sum, and express as a quotient of two integers.