1.77777778 as a Fraction

Professor Greenline Explaining Math Concepts

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Intermediate

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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, 1.77777778. We are going to learn how to convert a decimal to a fraction.

What is 1.77777778 as a Fraction?

$1.77777778 as a fraction$ Answer

The answer for 1.77777778 as a fraction is 16/9.

Explanation

Converting a decimal to a fraction is a task for students that can be done easily. You can follow the steps mentioned below to find the answer.

Step 1: Recognize that 1.77777778 is a repeating decimal. To express it accurately, use 1.777... (with the 7 repeating), which is equivalent to 1 + 0.777...

Step 2: Let x = 0.777..., which can be expressed as x = 0.777... = 7/9 (since 0.777... is a repeating decimal of 7, which is 7/9).

Step 3: Therefore, 1.777... = 1 + 7/9 = 9/9 + 7/9 = 16/9.

Thus, 1.77777778 can be written as the fraction 16/9.

Important Glossaries for 1.77777778 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.