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What Is 1/32 as a Decimal + Solution With Free Steps

The fraction 1/32 as a decimal is equal to 0.031.

Fractions are rational numbers expressed as the division of two numbers p and q as p/q, with p being the numerator and q being the denominator. There are multiple types of fractions including proper (q > p), improper (q < p), mixed fractions, etc. The given fraction 1/32 is a proper fraction because 32 > 1.

Here, we are interested more in the types of division that results 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 1/32.

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 seen done as follows:

Dividend = 1

Divisor = 32

Now, we introduce the most important quantity in our process of division, this is 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 $\div$ 32

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

Figure 1

1/32 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 32 we can see how 1 is Smaller than 32, and to solve this division we require that 1 be Bigger than 32.

This is done by multiplying the dividend by 10 and checking whether it is bigger than the divisor or not. And if it is then we calculate the Multiple of the divisor which is closest to the dividend and subtract it from the Dividend. This produces the Remainder which we then use as the dividend later.

In this case, 1 multiplied by 10 gets us 10, which is still smaller than 32. Therefore, we again multiply by 10 to get 100, which is greater than 32. To indicate these two multiplications, we add a decimal “.” and a 0 to our quotient.

Now, we begin solving for our dividend 1, which after getting multiplied by 100 becomes 100.

We take this 100 and divide it by 32, this can be seen done as follows:

 100 $\div$ 32 $\approx$ 3

Where:

32 x 3 = 96

We add 3 to our quotient. This will lead to the generation of a Remainder equal to 100 – 96 = 4, now this means we have to repeat the process by Converting the 4 into 40 and solving for that:

40 $\div$ 32 $\approx$ 1 

Where:

32 x 1 = 32

We add 1 to our quotient. Finally, combining all the three pieces of the Quotient, we get 0.031, with a Remainder equal to 8.

Images/mathematical drawings are created with GeoGebra.

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