# What Is 1/9 as a Decimal + Solution With Free Steps

**The fraction 1/9 as a decimal is equal to 0.111.**

**Decimal Numbers** are indeed very special as they can express numbers on the number line that lies between **Integers**. Therefore, they can be of great use in the **Real World** as things are not all fixed and certain like integers.

Now, as these numbers lie between integer values, their corresponding **Fractions** are not very easily solved. But there is always a method, and so we have **Long Division** for solving difficult divisions.

**Fractions** are widely known as smaller pieces of bigger objects and that is true for numbers as well. So when we have a fraction such as 1/9, it will result in a **Decimal Value**, and to find that decimal value, we shall solve this through **Division**.

## Solution

Solving a fraction starts by **Transforming** it into a division, and we know that a division has dividends and divisors. Therefore, the numerator 1 now becomes the **Dividend**, and the denominator 9 now becomes the **Divisor**.

**Dividend = 1**

**Divisor = 9**

Now, if we divide 1 by 9, it means to **Break** the number 1 into nine pieces, and take one of those pieces, hence a fraction of 1. As the transformation is completed the **Quotient** of this division would look like this:

**Quotient = Dividend $\div$ Divisor = 1 $\div$ 9**

Let’s find the solution to our fraction using the **Long Division Method**:

Figure 1

## 1/9 Long Division Method

This method works by finding the **Closest Multiple** of the divisor to the dividend and subtracting that multiple from the **Dividend**. The subtraction will result in a number which will be the **Remainder**, and this will become the new dividend as the division proceeds.

Now, when solving a division using **Long Division**, at some point the dividend will become smaller than the divisor, and that is when we introduce the **Decimal Point**. The decimal point will come into play in the **Quotient** and the dividend will be multiplied by 10.

Thus, we take a look at our fraction where the dividend is 1 **Smaller** than the divisor 9, so we have no choice but to introduce the **Decimal Point**. The whole number will therefore be 0, and the dividend will become 10. Now, let’s solve this:

**10 $\div$ 9 $\approx$ 1**

Where:

**9 x 1 = 9**

Hence, a **Remainder** of 10 – 9 = 1 was produced, as we have a remainder, we shall repeat the process and multiply another ten to the dividend. This makes the **Dividend** equal to 10 again. So, solving this results in:

**10 $\div$ 9 $\approx$ 1**

Where:

**9 x 1 = 9**

A **Remainder** of 10 – 9 = 1 is produced again, and we can see that the remainder is the same as the last time, and so will be the **Quotient**. Hence, we can conclude our division here and say that this is a **Repeating Decimal Number** with the repeating number being 1 and the **Quotient** being **0.111**.

*Images/mathematical drawings are created with GeoGebra.*