0.7777777 as a Fraction

Answer

The answer for 0.7777777 as a fraction will be 7/9.

Explanation

Converting a repeating decimal to a fraction involves recognizing the repeating part and following a structured approach. You can follow the steps mentioned below to find the answer.

Step 1: Let x = 0.7777777... (the repeating decimal).

Step 2: Since one digit is repeating, multiply by 10 to shift the decimal point one place to the right: 10x = 7.7777777...

Step 3: Subtract the original x from this equation to eliminate the repeating part: 10x - x = 7.7777777... - 0.7777777... 9x = 7

Step 4: Solve for x by dividing both sides by 9: x = 7/9

Thus, 0.7777777 can be written as a fraction 7/9.

• Fraction: A numerical quantity that is not a whole number, representing a part of a whole.

• Decimal: A number that uses the base ten and includes a decimal point to separate the whole part from the fractional part.

• Repeating Decimal: A decimal in which one or more digits repeat infinitely.

• Numerator: The top part of a fraction, indicating how many parts of the whole are being considered.

• Denominator: The bottom part of a fraction, showing how many parts make up a whole.