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.

37 48 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 37/48.


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

Figure 1

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


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


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


48 x 8 = 384

Finally, we have a Quotient generated as 0.7708, with a Remainder equal to 16.Pie Chart 37 by 48 Long Division Method

Images/mathematical drawings are created with GeoGebra. 

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