1.666666666 as a Fraction

Professor Greenline Explaining Math Concepts

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Numbers can be categorized into different types. A fraction is one of its kinds. 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. Numbers in decimal form are expressed with a decimal point (.), for example, 1.666666666. We are going to learn how to convert a decimal to a fraction.

What is 1.666666666 as a Fraction?

$1.666666666 as a fraction$

Answer

The answer for 1.666666666 as a fraction will be 5/3.

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: Firstly, any repeating decimal should be expressed in fractional form. Here, 1.666666666 is a repeating decimal. Let x = 1.666666666...

Step 2: Multiply both sides of the equation by 10 to shift the decimal point one place to the right. 10x = 16.666666666...

Step 3: Subtract the original equation (x = 1.666666666...) from this new equation. 10x - x = 16.666666666... - 1.666666666... 9x = 15

Step 4: Solve for x by dividing both sides by 9. x = 15/9

Step 5: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 3. 15/9 = 5/3

Thus, 1.666666666 can be written as the fraction 5/3.

Important Glossaries for 1.666666666 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.