0.06666666666 as a Fraction

Professor Greenline Explaining Math Concepts

Numbers can be categorized into different types. A fraction is one such type. 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 are expressed with a decimal point (.), for example, 0.06666666666. We are going to learn how to convert a decimal to a fraction.

0.06666666666 as a Fraction for US Students

What is 0.06666666666 as a Fraction?

$0.06666666666 as a fraction$

Answer

The answer for 0.06666666666 as a fraction is 2/30, which simplifies to 1/15.

Explanation

Converting a repeating decimal to a fraction is a task that students can accomplish with ease. You can follow the steps mentioned below to find the answer.

Step 1: Identify the repeating part of the decimal. Here, 0.06666666666 has a repeating part of '6'.

Step 2: Let x = 0.06666666666...

Step 3: Multiply by 10 to shift the decimal point for the repeating digits. So, 10x = 0.6666666666...

Step 4: Subtract the original x from this equation: 10x - x = 0.6666666666... - 0.06666666666...

Step 5: This simplifies to 9x = 0.6

Step 6: Therefore, x = 0.6/9

Step 7: Simplify the fraction by multiplying both the numerator and denominator by 10 to remove the decimal: x = 6/90 which simplifies to 1/15

Thus, 0.06666666666 can be written as the fraction 1/15.

Important Glossaries for 0.06666666666 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.