Rewrite as a simplified fraction.0.67 where 7 repeats forever.

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Carroll Marshall · Accepted Answer

Step 1: Let $$x = 0.67777\ldots $$ (where 7 repeats forever). Step 2:Multiply $$x$$ by 10 to shift the decimal point: $$10x = 6.77777\ldots $$ Step 3:Subtract the original $$x$$ from this equation: $$10x - x = 6.77777\ldots - 0.67777\ldots $$ Step 4:Solve for $$x$$:$$9x = 6.1$$$$x = \frac { 6.1} { 9} $$ Step 5:Simplify the fraction: $$\frac { 6.1} { 9} = \frac { 61} { 90} $$ Supplemental Knowledge:Converting a repeating decimal to a fraction involves a few algebraic steps. For the repeating decimal 0.6777... (where 7 repeats forever), we can represent it as $$x = 0.6777...$$. By multiplying both sides of the equation by 10, we shift the decimal point one place to the right, giving us $$10x = 6.777...$$.  Life in Context:Imagine baking and need to measure out ingredients accurately using fractions instead of decimals for accuracy in your recipe book. Knowing how to convert repeating decimals to fractions ensures accurate measurements every time - eliminating potential mishaps from occurring during culinary creations!For instance, if a recipe calls for an ingredient amounting to approximately 0.6777 cups, converting this to $$\frac { 61} { 90} $$ cups allows you to measure more accurately using standard measuring tools.Want to master converting decimals and other mathematical concepts with ease? UpStudy offers an array of calculators and learning resources tailored just for you! For all your math needs, including simplifying fractions or understanding complex numbers, explore UpStudy’s AI-powered problem-solving tools and live tutor sessions today, including a Fractions calculator. Dive deeper into mathematics and enhance your skills with UpStudy!$$\frac { 61} { 90} $$.

Rewrite as a simplified fraction.0.67 where 7 repeats forever.

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