0.77777778 as a Fraction

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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. Fraction represents a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2, the numbers in decimal are expressed with a decimal point (.), For example, 0.77777778, we are going to learn how to convert a decimal to a fraction.

What is 0.77777778 as a Fraction?

$0.77777778 as a fraction$

Answer

The answer for 0.77777778 as a fraction will be 7/9.

Explanation

Converting a repeating decimal to a fraction involves recognizing the repeating sequence and using algebraic methods. You can follow the steps mentioned below to find the answer.

Step 1: Identify the repeating part of the decimal. Here, 0.77777778 has the repeating part '7'.

Step 2: Let x = 0.77777778, then multiply both sides by 10 to position the decimal point after the first repeat. 10x = 7.77777778

Step 3: Subtract the original equation from this new equation to eliminate the repeating part. 10x - x = 7.77777778 - 0.77777778 9x = 7

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

Thus, 0.77777778 can be written as a fraction 7/9.

Important Glossaries for 0.77777778 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 a digit or group of digits repeats 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.