What Is 13/54 as a Decimal + Solution With Free Steps
The fraction 13/54 as a decimal is equal to 0.2407.
The decimal form and the fractional form are interchangeable. We can convert the fractional form into the decimal form by performing the long division. When the long division is performed on the fraction 13/54 it generates the non-terminating 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 13/54.
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 = 54
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 $\div$ 54
This is when we go through the Long Division solution to our problem. The solution for fraction 13/54 is shown in the figure below.
13/54 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 54, we can see how 13 is Smaller than 54, and to solve this division, we require that 13 be Bigger than 54.
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 54; this can be done as follows:
130 $\div$ 54 $\approx$ 2
54 x 2 = 108
This will lead to the generation of a Remainder equal to 130 – 108 = 22. Now this means we have to repeat the process by Converting the 22 into 220 and solving for that:
220 $\div$ 54 $\approx$ 4
54 x 4 = 216
This, therefore, produces another Remainder which is equal to 220 – 216 = 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 54. 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 54.
400 $\div$ 54 $\approx$ 7
54 x 7 = 378
Finally, we have a Quotient generated as 0.2407, with a Remainder equal to 22.
Images/mathematical drawings are created with GeoGebra.