# What Is 1/89 as a Decimal + Solution With Free Steps

**The fraction 1/89 as a decimal is equal to 0.011.**

We commonly encounter the **division** operation in real-life. The usual notation **p** $\boldsymbol\div$** q** is a little confusing in some cases like the division of long terms and in tables. **Fractions** are another way of expressing division in a compact form **p/q**, where p is called the **numerator** and q is termed the **denominator**.

Here, we are more interested in the division types that result in a **Decimal** value, as this can be expressed as a **Fraction**. We see fractions as a way of showing two numbers having the operation of **Division** between them that result in a value that lies between two **Integers**.

Now, we introduce the method used to solve said fraction to decimal conversion, called **Long Division, **which we will discuss in detail moving forward. So, let’s go through the **Solution** of fraction **1/89**.

## Solution

First, we convert the fraction components, i.e., the numerator and the denominator, and transform them into the division constituents, i.e., the **Dividend** and the **Divisor,** respectively.

* This can be done as follows:*

**Dividend = 1**

**Divisor = 89**

Now, we introduce the most important quantity in our division process: the **Quotient**. The value represents the **Solution** to our division and can be expressed as having the following relationship with the **Division** constituents:

**Quotient = Dividend $\div$ Divisor = 1 $\div$ 89**

This is when we go through the **Long Division** solution to our problem.

## 1/89 Long Division Method

We start solving a problem using the **Long Division Method** by first taking apart the division’s components and comparing them. As we have **1** and **89,** we can see how **1** is **Smaller** than **89**, and to solve this division, we require that 1 be **Bigger** than 89.

This is done by **multiplying** the dividend by **10** and checking whether it is bigger than the divisor or not. If so, we calculate the Multiple of the divisor closest to the dividend and subtract it from the **Dividend**. This produces the **Remainder,** which we then use as the dividend later.

In our case, however, multiplying 1 by 10 gets us 10, which is still smaller than 89. Therefore, we **multiply again by 10** to get **10 x 10 =** **100**, which is now larger than 89. To indicate this second multiplication by 10, we add a **0** directly after the **decimal point** in the quotient.

Now, we begin solving for our dividend **1**, which after getting multiplied by **10** becomes **100**.

*We take this 100 and divide it by 89; this can be done as follows:*

** 100 $\div$ 89 $\approx$ 1**

Where:

**89 x 1 = 89**

This will lead to the generation of a **Remainder** equal to **100 – 89 = 11**. Now this means we have to repeat the process by **Converting** the **11** into **110** and solving for that:

**110 $\div$ 89 $\approx$ 1 **

Where:

**89 x 1 = 89**

This, therefore, produces another **Remainder** which is equal to **110 – 89 = 21**. Since we have three decimal places, we stop the division process and combine the three pieces of the **Quotient** as **0.011**, with a final **remainder** equal to **21**.

*Images/mathematical drawings are created with GeoGebra.*