Write the repeating decimal as a fraction. .496496496 ______

Rephrase Problem: Let's first rephrase the ＂How can the repeating decimal 0.496496496... be expressed as a fraction?＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits 496 repeat indefinitely, so we can write the decimal as 0.496496496...Assign Variable: Let x equal the repeating decimal, so x = 0.496496496...Shift Decimal Point: Multiply x by 1000 to shift the decimal point three places to the right, since there are three digits in the repeating pattern. This gives us 1000x = 496.496496496...Subtract Original: Now subtract the original x from 1000x to eliminate the repeating decimals. This gives us 1000x - x = 496.496496496... - 0.496496496...Solve Equation: Perform the subtraction: 1000x - x = 999x and 496.496496496... - 0.496496496... = 496. This results in the equation 999x = 496.Divide to Simplify: Solve for x by dividing both sides of the equation by 999. This gives us x = 496/999.Check if the fraction 496/999 can be simplified. The numbers 496 and 999 do not have any common factors other than 1, so the fraction is already in its simplest form.

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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.

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.496496496

Rephrase Problem: Let's first rephrase the ＂How can the repeating decimal $0.496496496\ldots$ be expressed as a fraction?＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits $496$ repeat indefinitely, so we can write the decimal as $0.496496496\ldots$
Assign Variable: Let $x$ equal the repeating decimal, so $x = 0.496496496\ldots$
Shift Decimal Point: Multiply $x$ by $1000$ to shift the decimal point three places to the right, since there are three digits in the repeating pattern. This gives us $1000x = 496.496496496\ldots$
Subtract Original: Now subtract the original $x$ from $1000x$ to eliminate the repeating decimals. This gives us $1000x - x = 496.496496496... - 0.496496496...$
Solve Equation: Perform the subtraction: $1000x - x = 999x$ and $496.496496496... - 0.496496496... = 496$ . This results in the equation $999x = 496$ .
Divide to Simplify: Solve for $x$ by dividing both sides of the equation by $999$ . This gives us $x = \frac{496}{999}$ .
Divide to Simplify: Solve for $x$ by dividing both sides of the equation by $999$ . This gives us $x = \frac{496}{999}$ .Check if the fraction $\frac{496}{999}$ can be simplified. The numbers $496$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.