What Is 13/37 as a Decimal + Solution With Free Steps

The fraction 13/37 as a decimal is equal to 0.351.

A terminating decimal is a decimal that can be shown in a definite number. Moreover, in a terminating decimal, there is a definite decimal, like 0.12 is a terminating decimal, as the decimal comprises a finite number. The illustration of this example depicts the definition of terminating decimals.

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.

13 37 as a decimal

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 13/37.


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 = 37

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 $\div$ 37

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

13/37 Long Division Method

             Figure 1

13/37 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 37, we can see how 13 is Smaller than 37, and to solve this division, we require that 13 be Bigger than 37.

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 37; this can be done as follows:

 130 $\div$ 37 $\approx$ 3


37 x 3 = 111

This will lead to the generation of a Remainder equal to 130– 111 = 19. Now this means we have to repeat the process by Converting the 19 into 190 and solving for that:

190 $\div$ 37 $\approx$ 5


37 x 5= 185

This, therefore, produces another Remainder which is equal to 190 – 185 = 5. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 50.

50 $\div$ 37 $\approx$ 1


37 x 1 = 37

Finally, we have a Quotient generated after combining the three pieces of it as 0.351=z, with a Remainder equal to 13.

13 37 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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