What Is 5/64 as a Decimal + Solution With Free Steps

The fraction 5/64 as a decimal is equal to 0.078.

Fractions represent the operation of division of two numbers a and b in the form of the numeral a/b. Here, a is the numerator and b is the denominator. If the numerator is greater than the denominator, then the fraction is an improper fraction. Otherwise, it is a proper fraction. Therefore, 5/64 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.

5 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 5/64.

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 = 5

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 = 5 $\div$ 64

This is when we go through the Long Division solution to our problem. Given is the long division process in Figure 1:

5/64 Long Division Method

Figure 1

5/64 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 5 and 64, we can see how 5 is Smaller than 64, and to solve this division, we require that 5 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, 5 x 10 = 50, which is still smaller than 64. Therefore, we multiply by 10 again to get 50 x 10 = 500, which is now bigger than 64. To indicate this double multiplication by 10, we add a decimal “.” and 0 to our quotient.

Now, we begin solving for our dividend 5, which after getting multiplied by 100 becomes 500.

We take this 500 and divide it by 64; this can be done as follows:

 500 $\div$ 64 $\approx$ 7

Where:

64 x 7 = 448

This will lead to the generation of a Remainder equal to 500 – 448 = 52. Now this means we have to repeat the process by Converting the 52 into 520 and solving for that:

520 $\div$ 64 $\approx$ 8 

Where:

64 x 8 = 512

This, therefore, produces another Remainder which is equal to 520 – 512 = 8. As we have the three decimal places, we end up with a Quotient of 0.078 with a final remainder of 8.

5 64 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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