Rewriting Rational Numbers Exercise 4: (Theory ou pages \( 6-7 \) ) \( \begin{array}{lll}\text { 1) Without using a calculator write the following decimals as a fraction in their simplest fo } \\ \text { a) } 0,78 & \text { b) } 0,23 & \text { c) } 0,34\end{array} \) \( \begin{array}{lll}\text { a) Write the following recurrina }\end{array} \)
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Converting decimals to fractions can be a lot like translating a language! For example, 0.78 can be expressed as \( \frac{78}{100} \), and then simplified to \( \frac{39}{50} \). Similarly, 0.23 translates to \( \frac{23}{100} \) (can't get simpler than that!) and 0.34 becomes \( \frac{34}{100} \) which simplifies to \( \frac{17}{50} \). Each of these steps helps us transform a decimal into a tidy fraction, no calculator needed! When it comes to recurring decimals, they've got their own flair! Take 0.777... for instance; it keeps going with the number 7. To turn that into a fraction, you can set it as \( x = 0.777... \), then multiply by 10 to get \( 10x = 7.777... \). Subtract the first equation from the second (10x - x) and see how those repeating parts vanish, leading you to the elegant fraction \( \frac{7}{9} \). See? Math can be a magical world!