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What Is 25/52 as a Decimal + Solution With Free Steps

The fraction 25/52 as a decimal is equal to 0.4807.

Whenever a bigger thing is divided into equal smaller parts, the number of parts can be written in the form of a fraction. For example, if a hotel has 52 rooms out of which 25 are booked, so the ratio of booked rooms to the total is 25/52.

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 25/52.

Solution

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 = 25

Divisor = 52

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 = 25 $\div$ 52

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

25/52 Long Division Method

Figure 1

25/52 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 25 and 52, we can see how 25 is Smaller than 52, and to solve this division, we require that 25 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 25, which after getting multiplied by 10 becomes 250.

We take this 250 and divide it by 52; this can be done as follows:

 250 $\div$ 52 $\approx$ 4

Where:

52 x 4 = 208

This will lead to the generation of a Remainder equal to 250 – 208 = 42. Now this means we have to repeat the process by Converting the 42 into 420 and solving for that:

420 $\div$ 52 $\approx$ 8 

Where:

52 x 8 = 416

This, therefore, produces another Remainder equal to 420 – 416 = 4. Now again we multiply the dividend 4 by 10 and get 40 as a result. The dividend is still greater than the divisor which means the division is not possible.

Once again it is multiplied by 10 and for this, a zero is added to the quotient at the third place. Now we repeat the process for the dividend 400.

400 $\div$ 52 $\approx$ 7 

Where:

52 x 7 = 364

Finally, we have a Quotient generated after combining the four pieces of it as 0.4807, with a Remainder equal to 36.

Images/mathematical drawings are created with GeoGebra.

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