118 LearnersLast updated on May 26th, 2025
0.7777777 as a Fraction
Numbers can be categorized into different types. Fraction is one of its kind. It is always represented in the form of p/q, where p is the numerator and q is the denominator. A fraction represents a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2. Decimals are expressed with a decimal point (.), for example, 0.7777777. We are going to learn how to convert a repeating decimal to a fraction.
What is 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.
Important Glossaries for 0.7777777 as a Fraction
- 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.
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