What Is 1/52 as a Decimal + Solution With Free Steps

The fraction 1/52 as a decimal is equal to 0.019.

The fractions are represented in the form of p/q where ‘p‘ is the numerator and ‘d‘ is the denominator. The fractions can be categorized as proper, improper, and mixed fractions. As the numerator is smaller than the denominator in the provided fraction, so it is a proper fraction.

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.

1 52 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 1/52.


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 seen done as follows:

Dividend = 1

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 = 1 $\div$ 52

This is when we go through the Long Division solution to our problem. The solution is given in the figure below.

1/52 Long Division Method

Figure 1

1/52 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 1 and 52, we can see how 1 is Smaller than 52, and to solve this division, we require that 1 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 1, which after getting multiplied by 10 becomes 10.

But it is smaller than the division which is 52. To make it bigger than the divisor we multiply the dividend by 10 again by putting a zero in the quotient after the decimal point. Now we can perform the division.

We take this 100 and divide it by 52; this can be seen done as follows:

 100 $\div$ 52 $\approx$ 1


52 x 1 = 52

This will lead to the generation of a Remainder equal to 100 – 52 = 48. Now this means we have to repeat the process by Converting the 48 into 480 and solving for that:

480 $\div$ 52 $\approx$ 9 


52 x 2 = 468

This, therefore, produces another remainder which is equal to 480 – 468 = 12.

Finally, we have a Quotient generated after combining the three pieces of it as 0.019, with a Remainder equal to 12.

1 52 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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