# What Is 4/10 as a Decimal + Solution With Free Steps

**The fraction 4/10 as a decimal is equal to 0.4.**

A **Fraction** is a very special way of expressing a mathematical operation, it is equivalent to the **Dot** used in expressing multiplication. A **Fraction** is therefore generally used to express a division between two numbers, but it’s the kind of **Division** that doesn’t solve into an integer.

As we know, this kind of division is expressed as a fraction and doesn’t produce an **Integer**, we come to find that this division produces a **Decimal Value**. A Decimal number is best known as one which has two parts, a **Whole Number** part, and a **Decimal** part. Its value lies between two **Integers**.

So, we will solve the fraction given to us as 4/10 using the method for solving this kind of division, the** Long Division Method**.

## Solution

We start off solving a **Fraction** into a division by first converting a said fraction into a division. That is done by **Transforming** the components of a fraction into a division. As we know, the **Dividend** is equivalent to the numerator, and the **Divisor** is equivalent to the denominator. Hence, we express our **Fraction** now as:

**Dividend = 4**

**Divisor = 10**

Now, if we analyze the **Division** that we have, we conclude that 4 our **Dividend** is being broken down into 10 pieces. And one of those pieces is then expressed as the **Quotient** i.e., the **Solution** of this division. This is also what the **Fraction** was expressing, so we have:

**Quotient = Dividend $\div$ Divisor = 4 $\div$ 10**

Finally, we will go through the **Long Division Solution** to this problem:

Figure 1

## 4/10 Long Division Method

Solving a division using **Long Division**, we have to keep in mind two rules on which it operates. The **First Rule** is that when the dividend is **Smaller** than the divisor, we introduce the decimal point in the **Quotient** and multiply the dividend by 10. The **Second Rule** states that we find the Multiple of the divisor closest to the dividend and then **Subtract** the multiple from it.

Now the solution of the **Subtraction** then becomes the dividend for the next iteration of division, and it is called the **Remainder**. Also, once the **Decimal Point** is brought in, then we can always multiply the dividend by 10 if it’s **Smaller** than the divisor.

Finally, we look at our dividend of 4 **Smaller** than 10, so we have to make it bigger than the **Divisor**. We already know that under such circumstances we use the first rule of the **Long Division **and multiply the dividend by 10.

But this also adds a decimal point to the **Quotient**, and this means we have a quotient with 0 **Whole Number** and no **Decimal Number**. The **Dividend**, hence, becomes 40 and the solution is:

**40 $\div$ 10 = 4**

Where:

**10 x 4 = 40**

Therefore, no **Remainder** is generated, and a **Quotient** with a value of 0.4 is found.

*Images/mathematical drawings are created with GeoGebra.*