Write the repeating decimal as a fraction. .790790790 ______

Identify Repeating Decimal: Let's identify the repeating part of the decimal. The digits 790 repeat indefinitely, so we can express the repeating decimal as 0.790790790...Set Decimal as Variable: To convert this repeating decimal to a fraction, we can set it equal to a variable, let's say x: x = 0.790790790...Isolate Repeating Part: To isolate the repeating part, we can multiply x by 1000, since there are three digits in the repeating sequence: 1000x = 790.790790...Subtract and Simplify: Now, we subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 790.790790... - 0.790790790... This simplifies to: 999x = 790Divide to Find x: To find the value of x, we divide both sides of the equation by 999: x = 790 / 999Simplify Fraction: We can simplify the fraction by looking for common factors between the numerator and the denominator. In this case, there are no common factors other than 1, so the fraction is already in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $.790790790$

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Algebra 2

Write a repeating decimal as a fraction

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Q. Write the repeating decimal as a fraction.

\newline

.790790790

Identify Repeating Decimal: Let's identify the repeating part of the decimal. The digits $790$ repeat indefinitely, so we can express the repeating decimal as $0.790790790\ldots$
Set Decimal as Variable: To convert this repeating decimal to a fraction, we can set it equal to a variable, let's say $x$ : $x = 0.790790790\ldots$
Isolate Repeating Part: To isolate the repeating part, we can multiply $x$ by $1000$ , since there are three digits in the repeating sequence: $\newline$ $1000x = 790.790790\ldots$
Subtract and Simplify: Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part: $\newline$ $1000x - x = 790.790790... - 0.790790790...$ $\newline$ This simplifies to: $\newline$ $999x = 790$
Divide to Find x: To find the value of x, we divide both sides of the equation by $999$ : $\newline$ $x = \frac{790}{999}$
Simplify Fraction: We can simplify the fraction by looking for common factors between the numerator and the denominator. In this case, there are no common factors other than $1$ , so the fraction is already in its simplest form.