# 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.

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.