What is the repeating decimal 0.7777.... as a fraction in simplest form?
x = 0.7777...
10 x = 10 ∙ 0.7777... = 7.7777...
10 x - x = 7.7777... - 0.7777...
9 x = 7
Divide both sides by 9
x = 7 / 9
7 over 9 7/9
Yas
To find the fraction equivalent of the repeating decimal 0.7777..., we can follow these steps:
Step 1: Assign a variable to the repeating decimal. Let's call it "x".
x = 0.7777...
Step 2: Multiply both sides of the equation by a power of 10 to eliminate the repeating part.
10x = 7.7777...
Step 3: Subtract the original equation from the new equation to eliminate the repeating part.
10x - x = 7.7777... - 0.7777...
Simplifying, we get:
9x = 7
Step 4: Divide both sides of the equation by 9 to solve for "x".
x = 7/9
Therefore, the fractional equivalent of the repeating decimal 0.7777... is 7/9 in its simplest form.