3.16666 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. A 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, 3.16666, we are going to learn how to convert a decimal to a fraction.

What is 3.16666 as a Fraction?

$3.16666 as a fraction$

Answer

The answer for 3.16666 as a fraction will be 19/6.

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 decimal number should be converted to a fraction for easy calculation. Here, 3.16666 is the number on the numerator and the base number 1 will be the denominator. Then, 3.16666 becomes 3.16666/1.

Step 2: Since 3.16666 is a repeating decimal, we can express the repeating part as a fraction. Let x = 3.16666. Multiply both sides by 10000 to shift the repeating part: 10000x = 31666.66...

Step 3: Subtract the original equation from this new equation to eliminate the repeating part: 10000x - 10x = 31666.66... - 31.6666... 9990x = 31635

Step 4: Solve for x: x = 31635/9990

Step 5: Simplify the fraction by dividing both the numerator and denominator by their GCD, which is 15: 31635/9990 = 2109/666

Step 6: Further simplify by dividing both by 3: 2109/666 = 703/222

Step 7: Convert back to a mixed number: 703/222 = 3 19/222

Thus, 3.16666 can be written as the fraction 19/6.