# What Is 5/75 as a Decimal + Solution With Free Steps

**The fraction 5/75 as a decimal is equal to 0.066.**

A **Fraction** in arithmetic is defined as a thing that depicts the number of parts contained by a specific size. Moreover, a **Complex fraction** contains a fraction in the numerator or the denominator. At the same time, a Simple fraction contains both integers.

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 **5/75.**

## 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 = 5**

**Divisor = 75**

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 = 5 $\div$ 75**

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

## 5/75 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 **5 **and **75,** we can see how **5** is **Smaller** than **75**, and to solve this division, we require that 5 be **Bigger** than 75.

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.

Now, we begin solving for our dividend **5**, which after getting multiplied by **100** becomes** 500.**

*We take this 500 and divide it by 75; this can be done as follows:*

** 500 $\div$ 75 $\approx$ 6**

Where:

**75 x 6 = 450**

This will lead to the generation of a **Remainder** equal to **500 – 450 = 50.** Now this means we have to repeat the process by **Converting** the **50** into **500** and solving for that:

**500 $\div$ 75 $\approx$ 6**

Where:

**75 x 6 = 450**

This, therefore, produces another **Remainder** which is equal to **500 – 450 = 50.**

Finally, we have a **Quotient** generated after combining the three pieces of it as **0.066=z**, with a **Remainder** equal to **50.**

*Images/mathematical drawings are created with GeoGebra.*