# What Is 1/7 as a Decimal + Solution With Free Steps

**The fraction 1/7 as a decimal is equal to 0.142857.**

We use **Fractions** to express decimal numbers in terms of integers. As we know, **Decimal Numbers **cannot be expressed as integers, as they lie between two. So, how do we convert a fraction which contains two integers in a division into a **Decimal Number**?

The answer is simple, we use a method called **Long Division**. This method makes solving **Problems** of a such sort straightforward. A **Decimal Number** is composed of two components, one is the **Whole Number**, and the other one is the **Decimal** component.

So now let’s solve this problem using the **Long Division Method** and find its solution.

## Solution

We solve fractions into decimal numbers by first transforming them into **Division**. As we know, a fraction represents a division, we can also **Interchange** the components of a fraction with that of a division. This is done by replacing the label of the numerator with **Dividend**, and the denominator with **Divisor**. It can be seen done down here:

**Dividend = 1**

**Divisor = 7**

Now, the quantity named the **Quotient** is of great importance here, as it is produced as a result of the division between two numbers. Thus, for our **Fraction** expressed as 1/7, we will express the **Quotient** as:

**Quotient = Dividend $\div$ Divisor = 1 $\div$ 7**

Finally, let’s go through the **Long Division Solution** to this problem:

Figure 1

## 1/7 Long Division Method

To solve a problem by this method, we rely on the **Multiple** of the divisor, which is closest to the dividend. But that’s not all, when our dividend becomes **Smaller** than the divisor, we multiply it by ten and place a **Decimal Point** in the quotient.

Now we will introduce the last quantity of our interest, which is the **Remainder. **This is produced by **Subtracting** the multiple from the dividend. Also, this remainder becomes the **Dividend** after every iteration of the division.

Hence, looking at our dividend of 1, we see that it is **smaller** than the divisor, so we multiply it by ten, and place a **Decimal** in the quotient. This makes our dividend equal to 10, so let’s solve for 10/7:

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

Where:

** 7 x 1 = 7**

This leads to the generation of a **Remainder** equal to 10-7=3, so we repeat the process and get our new **Dividend** of 3 up to 30. Now, solving for 30/7 leads to:

**30 $\div$ 7 $\approx$ 4**

Where:

**7 x 4 = 28**

This then produces a **Remainder** of 30-28=2, which calls for us to repeat the process. And this time, we have 20/7 to solve:

**20 $\div$ 7 $\approx$ 2**

Where:

** 7 x 2 = 14**

Hence, we finally have a remainder of 20-14 = 6. We usually would stop right here as we have a value until the **Third Decimal Place, **but if we keep solving it to the sixth decimal place, we find that this **Quotient** will repeat itself, so we have **0.142857**.

*Images/mathematical drawings are created with GeoGebra.*