Change the infinite decimal [tex]0.577777\ldots[/tex] to a fraction.

x = 0.5777... ∣ m u lt i pl y b o t h s i d es b y 10 10 x = 5.777... ∣ m u lt i pl y b o t h s i d es b y 10 100 x = 57.777... mak e a d i ff ere n ce 100 x − 10 x : 90 x = 57.777... − 5.777... 90 x = 52 ∣ d i v i d e b o t h s i d es b y 90 x = 90 52 ​ x = 45 26 ​ 0.5777... = 45 26 ​ ​

Answered by Anonymous | 2024-06-10

Converting Infinite Decimals to Fractions
To convert an infinite decimal like 0.577777... to a fraction, we use the concept of repeating decimals. Here's a step-by-step method to complete this conversion:
Let x equal the infinite decimal: x = 0.577777...
Since there is one repeating digit after the decimal point, multiply x by 10 to shift the decimal one place to the right: 10x = 5.77777...
Now subtract the original x from this new equation: 10x - x = 9x = 5.77777... - 0.577777... = 5
Solve the equation for x: x = 5/9
This method can be applied to any repeating decimal, using multiplication by an appropriate power of 10 to match the length of the repeating sequence.

Answered by Qwlizard | 2024-06-24

The infinite decimal 0.57777... can be converted to the fraction 45 26 ​ by setting up an equation, multiplying, and solving for x .
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Answered by Anonymous | 2024-10-02