# What Is 13/42 as a Decimal + Solution With Free Steps

**The fraction 13/42 as a decimal is equal to 0.309523809.**

An important concept of mathematics is **Fraction**, that is simplified by division. **Division** which transforms a fraction into its decimal number, looks like the trickiest operation among all the mathematical operations. But it can be made easy using certain techniques.

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 **13/42.**

## 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 = 13**

**Divisor = 42**

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 = 13 $\div$ 42**

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

## 13/42 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 **13 **and **42,** we can see how **13 **is **Smaller** than **42**, and to solve this division, we require that 13 be **Bigger** than 42.

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 **13**, which after getting multiplied by **10** becomes **130**.

*We take this 130 and divide it by 42; this can be done as follows:*

** 130 $\div$ 42 $\approx$ 3**

Where:

**42 x 3 = 126**

This will lead to the generation of a **Remainder** equal to **130 – 126 = 4**. Now this means we have to repeat the process by **Converting** the **4 **into **40.**

Still, the dividend is less than the divisor, so we will multiply it by 10 again. For that, we have to add the **zero **in the **quotient**. So, by multiplying the dividend by **10 **twice in the same step and by adding **zero **after the decimal point in the **quotient**, we now have a dividend of **400**.

**400 $\div$ 42 $\approx$ 9 **

Where:

**42 x 9 = 378**

So, we have a **Quotient** generated after combining the pieces of it as **309=z**, with a **Remainder** equal to **22**.

*Images/mathematical drawings are created with GeoGebra.*