Write the repeating decimal as a fraction. .998998998 ______

Rephrase Problem: Let's first rephrase the problem into a single ＂How can the repeating decimal 0.998998998... be expressed as a fraction?＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂998＂ repeat indefinitely, so we can write the decimal as 0.998998998...Denote Decimal as x: Let's denote the repeating decimal as x: x = 0.998998998... To convert this into a fraction, we will multiply x by a power of 10 that moves the repeating digits to the left of the decimal point. Since there are three repeating digits, we multiply by 10^3 (which is 1000): 1000x = 998.998998998...Multiply by Power of 10: Now we have two equations: 1) x = 0.998998998... 2) 1000x = 998.998998998... Subtract the first equation from the second to eliminate the repeating decimals: 1000x - x = 998.998998998... - 0.998998998...Subtract Equations: Perform the subtraction: 1000x - x = 998 999x = 998Solve for x: Now, solve for x by dividing both sides of the equation by 999: x = 998 / 999Check Fraction: Check the fraction to ensure it is in simplest form. Since 998 and 999 have no common factors other than 1, the fraction 998/999 is already in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $.998998998$

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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

.998998998

Rephrase Problem: Let's first rephrase the problem into a single ＂How can the repeating decimal $0.998998998\ldots$ be expressed as a fraction?＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂ $998$ ＂ repeat indefinitely, so we can write the decimal as $0.998998998\ldots$
Denote Decimal as $x$ : Let's denote the repeating decimal as $x$ : $x = 0.998998998...$ $\newline$ To convert this into a fraction, we will multiply $x$ by a power of $10$ that moves the repeating digits to the left of the decimal point. Since there are three repeating digits, we multiply by $10^3$ (which is $1000$ ): $1000x = 998.998998998...$
Multiply by Power of $10$ : Now we have two equations: $\newline$ $1$ ) $x = 0.998998998\ldots$ $\newline$ $2$ ) $1000x = 998.998998998\ldots$ $\newline$ Subtract the first equation from the second to eliminate the repeating decimals: $\newline$ $1000x - x = 998.998998998\ldots - 0.998998998\ldots$
Subtract Equations: Perform the subtraction: $\newline$ $1000x - x = 998$ $\newline$ $999x = 998$
Solve for x: Now, solve for x by dividing both sides of the equation by $999$ : $x = \frac{998}{999}$
Check Fraction: Check the fraction to ensure it is in simplest form. Since $998$ and $999$ have no common factors other than $1$ , the fraction $\frac{998}{999}$ is already in its simplest form.