What Is 6/64 as a Decimal + Solution With Free Steps

The fraction 6/64 as a decimal is equal to 0.093.

When we divide two numbers p and q, where p is the dividend and q is the divisor, then we get either an integer or decimal value as a result. An integer appears if p is a multiple of q and p > q. If either of these conditions is not satisfied, we end up with the decimal result.

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.

6 64 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 6/64.


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 = 6

Divisor = 64

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 = 6 $\div$ 64

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

6/64 Long Division Method

Figure 1

6/64 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 6 and 64, we can see how 6 is Smaller than 64, and to solve this division, we require that 6 be Bigger than 64.

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.

In our case, 6 x 10 = 60 which is still smaller than 64. Thus, we must again multiply by 10 such that 60 x 10 = 600, which is bigger than 64. However, we have to add a 0 to our quotient for the second multiplication because 60 is not divisible by 4 (hence the multiplication with 0 and its addition to the quotient). 

Now, we begin solving for our dividend 6, which after getting multiplied by 10 becomes 600.

We take this 600 and divide it by 64; this can be done as follows:

 600 $\div$ 64 $\approx$ 9


64 x 9 = 576

This will lead to the generation of a Remainder equal to 600 – 576 = 24. Now this means we have to repeat the process by Converting the 24 into 240 and solving for that:

240 $\div$ 64 $\approx$ 3 


64 x 3 = 192

This, therefore, produces another Remainder which is equal to 240 – 192 = 48. Since we have three decimal places now, we combine them to get the final Quotient as 0.093 with a final remainder of 48.

6_64 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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