What Is 7/52 as a Decimal + Solution With Free Steps
The fraction 7/52 as a decimal is equal to 0.13461538.
A fraction represents dividing or splitting something into equal parts which may result in a whole complete number as an integer or decimal, like fraction 6/2 results in 3 (integer) equal parts however 10/4 results in 2.5 (decimal) equal parts.
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 7/52.
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 = 7
Divisor = 52
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 = 7 $\div$ 52
This is when we go through the Long Division solution to our problem. The following figure shows the long division:
7/52 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 7 and 52, we can see how 7 is Smaller than 52, and to solve this division, we require that 7 be Bigger than 52.
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 7, which after getting multiplied by 10 becomes 70.
We take this 70 and divide it by 52; this can be done as follows:
70 $\div$ 52 $\approx$ 1
52 x 1 = 52
This will lead to the generation of a Remainder equal to 70 – 52 = 18. Now this means we have to repeat the process by Converting the 18 into 180 and solving for that:
180 $\div$ 52 $\approx$ 3
52 x 3 = 156
This, therefore, produces another Remainder equal to 180– 156 = 24. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 240.
240 $\div$ 52 $\approx$ 4
52 x 4 = 208
Finally, we have a Quotient generated after combining the three pieces of it as 0.134=z, with a Remainder equal to 32.
Images/mathematical drawings are created with GeoGebra.