What Is 15/38 as a Decimal + Solution With Free Steps

The fraction 15/38 as a decimal is equal to 0.39473684.

A fraction represents the part of a whole. The fractional form can be converted to its equivalent decimal form. Fractions are mostly used to represent rational numbers. The fraction 15/38 is a proper fraction because its denominator is greater than its numerator.

15 38 as a decimal

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 15/38.


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 = 15

Divisor = 38

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 = 15 $\div$ 38

This is when we go through the Long Division solution to our problem. The following figure shows the long division:

15/38 Long Division Method

Figure 1

15/38 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 15 and 38, we can see how 15 is Smaller than 38, and to solve this division, we require that 15 be Bigger than 38.

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 15, which after getting multiplied by 10 becomes 150.

We take this 150 and divide it by 38; this can be done as follows:

 150 $\div$ 38 $\approx$ 3


38 x 3 = 114

This will lead to the generation of a Remainder equal to 150 – 114 = 36. Now this means we have to repeat the process by Converting the 36 into 360 and solving for that:

360 $\div$ 38 $\approx$ 9 


38 x 9 = 342

This, therefore, produces another Remainder equal to 360 – 342 = 18. Now we must solve this problem to the Third Decimal Place for accuracy, so we repeat the process with dividend 180.

180 $\div$ 38 $\approx$ 4 


38 x 4 = 152

Finally, we have a Quotient generated after combining the three pieces of it as 0.394=z, with a Remainder equal to 28.Quotient and Remainder of 15 per 38

Images/mathematical drawings are created with GeoGebra.

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