Question
Write the following infinite decimal expansion as a fraction. You do not need to simplify. [Click for Help Video](10 points)
0.366¯¯¯¯¯¯¯¯=
Let's represent the infinite decimal expansion as a variable:
0.366¯¯¯¯¯¯¯¯ = x
To find x, we can multiply both sides of the equation by a power of 10 that will eliminate the repeating decimal. In this case, we'll multiply both sides by 1000 to eliminate the repeating part:
1000 * 0.366¯¯¯¯¯¯¯¯ = 1000x
This simplifies to:
366.366¯¯¯¯¯¯¯¯ = 1000x
Now, we can subtract the original equation from this new equation to eliminate the repeating part:
366.366¯¯¯¯¯¯¯¯ - 0.366¯¯¯¯¯¯¯¯ = 1000x - x
This simplifies to:
366 = 999x
To solve for x, we divide both sides of the equation by 999:
x = 366/999
Therefore, the infinite decimal expansion 0.366¯¯¯¯¯¯¯¯ is equivalent to the fraction 366/999.