**What Is 37/48 as a Decimal + Solution With Free Steps**

**The fraction 37/48 as a decimal is equal to 0.7708.**

A fraction is considered to be the** ratio** of two numbers. The fraction consists of a numerator and denominator. The fractional form is difficult to use in solving mathematical problems. Therefore the fraction is converted into its equivalent representation. It is known as the **decimal **representation.

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 **37/48**.

**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 = 37**

**Divisor = 48**

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 = 37 $\div$ 48**

This is when we go through the **Long Division** solution to our problem. The solution for fraction 37/48 is shown in the following figure.

**37/48 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 **37** and **48,** we can see how **37** is **Smaller** than **48**, and to solve this division, we require that 37 be **Bigger** than 48.

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 **37**, which after getting multiplied by **10** becomes **370**.

*We take this **370** and divide it by **48**; this can be done as follows:*

** 370 $\div$ 48 $\approx$ 7**

Where:

**48 x 7 = 336**

This will lead to the generation of a **Remainder** equal to **370 – 336 = 34**. Now this means we have to repeat the process by **Converting** the **34** into **340** and solving for that:

**340 $\div$ 48 $\approx$ 7**

Where:

**48 x 7 = 336**

This, therefore, produces another **Remainder** which is equal to **340 – 336 = 4**. Now we must solve this problem to **Third Decimal Place** for accuracy.

However, **4** when multiplied by 10 becomes 40 which is still smaller than 48. Therefore we will multiply 40 by 10 again and add a zero in the quotient after the decimal point. By doing this the dividend will become 400 which is bigger than 48.

**400 $\div$ 48 $\approx$ 8**

Where:

**48 x 8 = 384**

Finally, we have a **Quotient** generated as **0.7708**, with a **Remainder** equal to **16**.

*Images/mathematical drawings are created with GeoGebra. *