# What Is 2/3 as a Decimal + Solution With Free Steps

**The fraction 2/3 as a decimal is equal to 0.666.**

**Fractions** are widely known for expressing the operation of division occurring between two numbers, but they represent a very special kind of division. This **Division** cannot be solved using the traditional method and thus requires a new technique.

This new technique is called the **Long Division Method**, and it is known for solving division problems in pieces. Solving a problem using this method leads to a **Decimal Value** to be produced as its result.

Now, let’s take a deeper dive into the solution of our fraction 2/3.

## Solution

The first step in solving a problem such as 2/3 into a **Decimal Value** is that we separate the constituents of the fraction and convert them into the **Division** components. This is done by transforming the numerator into the **Dividend** and the denominator into the **Divisor**.

This is done as follows:

**Dividend = 2**

**Divisor = 3**

This is when we introduce the quantity known as the **Quotient**, it represents the solution to a division problem. And we find it by applying the **Division** operation between the two numbers referred to as **Dividend** and the **Divisor**:

**Quotient = Dividend $\div$ Divisor = 2 $\div$ 3**

Now, to find out the **Quotient** of this fraction transformed into a division; we shall solve this problem using the **Long Division Method**:

Figure 1

## 2/3 Long Division Method

We start by understanding the process of **Long Division**, it works by placing a decimal point after the **Whole Number** of the Quotient. Placing this **Decimal Point** gives us the ability to multiply 10 by every dividend.

The **Whole Number** in the Quotient is the number that corresponds to the non-decimal part of the Quotient so for a **proper fraction** it is 0 and for **Improper**, otherwise.

Finally, we have a **Remainder** produced after each division iteration, and this number then becomes the new **Dividend** to be solved in the next iteration. We run at least three iterations to get the most **accurate** result.

Taking a look at our numerator 2 we see that this is a **proper fraction**, and so we multiply the dividend with 10 and get 20. The **Quotient** now contains the 0 and the decimal point, and now we shall solve for this dividend:

**20 $\div$ 3 $\approx$ 6**

Where:

**3 x 6 = 18 **

Hence, a **Remainder** of 20-18 = 2 is produced, and we repeat the process now 2 is the dividend and we multiply 10 with it and solve:

**20 $\div$ 3 $\approx$ 6**

Where:

**3 x 6 = 18 **

Now, as we can see the **Remainder** is repeating itself, 20 – 18 = 2, this is a repeating decimal number, and the **Quotient** when compiled together results in 0.666. And it will keep repeating its value until infinity.

*Images/mathematical drawings are created with GeoGebra.*