What Is 7/64 as a Decimal + Solution With Free Steps

The fraction 7/64 as a decimal is equal to 0.109375.

When converting Fractional quantities to Decimal values, the division operator is needed. The lower portion of the fraction is referred to as the Denominator, and the upper portion is known as the Numerator.

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.

7 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 7/64.


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 = 7

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 = 7 $\div$ 64

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

7/64 Long Division Method

Figure 1

7/64 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 7 and 64, we can see how 7 is Smaller than 64, and to solve this division, we require that 7 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.

Now, we begin solving for our dividend 7, which after getting multiplied by 10 becomes 70.

We take this 70 and divide it by 64; this can be done as follows:

 70 $\div$ 64 $\approx$ 1


64 x 1 = 64

This will lead to the generation of a Remainder equal to 70 – 64 = 6. Now this means we have to repeat the process by Converting the 6 into 60.

Still, the dividend is less than the divisor, so we will multiply it by 10 again. For that, we have to add the zero in the quotient. So, by multiplying the dividend by 10 twice in the same step and by adding zero after the decimal point in the quotient, we now have a dividend of 600.

600 $\div$ 64 $\approx$ 9 


64 x 9 = 576

This, therefore, produces another Remainder which is equal to 600 – 576 = 24.

Finally, we have a Quotient generated after combining the pieces of it as 0.109=z, with a Remainder equal to 24.

7 64 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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