# What Is 4/7 as a Decimal + Solution With Free Steps

**The fraction 4/7 as a decimal is equal to 0.571.**

**Division**, out of all the mathematical operations, seems to be the most complicated one. But it doesn’t have to be, as there is a way to solve this seemingly difficult problem. The method in question for solving fractions is called **Long Division**.

In this guide, we will solve the given fraction i.e., 4/7 using **Long Division** as it will produce the decimal equivalent for this fraction.

## Solution

We begin by first separating the constituents of the fraction based on the nature of their operation. The numerator in a fraction in the case of a division is called the **Dividend**, whereas the denominator is referred to as the **Divisor**. And this brings us to this result:

**Dividend = 4**

**Divisor = 7 **

Now, we carry on by rearranging this fraction in a more descriptive fashion, where we also introduce the term **Quotient** which corresponds to the solution of a division:

**Quotient = Dividend $\div$ Divisor = 4 $\div$ 7 **

Now, we can solve the problem as follows using Long Division:

Figure 1

## 4/7 Long Division Method

The **Long Division Method** used to solve this problem can be further looked into as follows.

We had:

**4 $\div$ 7 **

As we know, 7 is greater than 4, and therefore you can’t solve this division without introducing a **Decimal Point**. Now to introduce said decimal point, we plug in a zero to the right of our **Remainder**.

Now **Remainder** is another division-specific term used for the remaining value resulting from an incomplete division.

In this case, 4 is a remainder, so we will introduce the **Zero** to its right, therefore turning it into 40 in the process. Now, we solve for:

**40 $\div$ 7 $\approx$ 5**

Where:

** 7 x 5 = 35 **

This means that there is a** Remainder** produced from this division as well, and it is equal to 40 – 35 = 5.

Having produced a remainder from the **Division**, we repeat the process and plug a zero to the **Remainder’s Right**. In this case, we don’t have to use another decimal point given that the **Quotient** is already a decimal value now.

The resulting remainder was 5, so the addition of a** Zero** to its right will produce 50. Now we can move forward and calculate:

**50 $\div$ 7 $\approx$ 7**

Where:

** 7 x 7 = 49 **

Thus, we have another **Remainder** equal to 1. Bringing in another zero will produce 10, so to solve up to three decimal places we must calculate:

**10 $\div$ 7 $\approx$ 1**

Where:

**7 x 1 = 7 **

Thus, we have a **Quotient** equal to 0.571 with a **Remainder** of 3. This means that if we solve any further, we may be able to get a more accurate result.

*Images/mathematical drawings are created with GeoGebra.*