7777 Repeating as a Fraction
The repeating decimal 7777 can be represented as a fraction. Here's how to convert it:
1. Set up an equation:
Let x equal the repeating decimal:
x = 0.7777...
2. Multiply both sides by 10:
10x = 7.7777...
3. Subtract the first equation from the second equation:
10x = 7.7777...
- x = 0.7777...
9x = 7
4. Solve for x:
x = 7/9
Therefore, the repeating decimal 0.7777... is equivalent to the fraction 7/9.
Explanation:
The trick here is to shift the decimal point one place to the right by multiplying by 10. Subtracting the original equation eliminates the repeating part, leaving a simple equation to solve. This method works for any repeating decimal.
