How do you convert 0.7777 as a fraction?

To convert the decimal 0.7777 into a fraction, follow these steps:

Step 1: Identify the Decimal

The decimal 0.7777 is a repeating decimal, where the digit 7 repeats indefinitely.

Step 2: Set Up the Equation

Let x equal the decimal:

x = 0.7777...

Step 3: Eliminate the Repeating Part

To remove the repeating decimal, multiply both sides of the equation by 10:

10x = 7.7777...

Step 4: Subtract the Original Equation

Now, subtract the original equation from this new equation:

10x - x = 7.7777... - 0.7777...

This simplifies to:

9x = 7

Step 5: Solve for x

Now, divide both sides by 9:

x = 7/9

Final Result

The decimal 0.7777 as a fraction is 7/9.