 # What Is 49/64 as a Decimal + Solution With Free Steps

The fraction 49/64 as a decimal is equal to 0.765.

Decimal Numbers are divided into Like Decimal and Unlike Decimal Numbers categories. These decimal numbers are referred to as unlike decimal numbers since they do not have the same number of digits following the decimal point. For instance, the decimal numbers 1.23 and 1.898 are unlike because the former contains two digits and the latter has three digits following the decimal point.

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. 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 49/64.

## 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 = 49

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 = 49 $\div$ 64

This is when we go through the Long Division solution to our problem. Figure 1 shows the long division method: Figure 1

## 49/64 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 49 and 64, we can see how 49 is Smaller than 64, and to solve this division, we require that 49 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 49, which after getting multiplied by 10 becomes 490.

We take this 490 and divide it by 64; this can be done as follows:

490 $\div$ 64 $\approx$ 7

Where:

64 x 7 = 448

This will lead to the generation of a Remainder equal to 490 – 448 = 42. Now this means we have to repeat the process by Converting the 42 into 420 and solving for that:

420 $\div$ 49 $\approx$ 6

Where:

49 x 6 = 384

This, therefore, produces another Remainder which is equal to 420 – 384 = 36. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 360.

360 $\div$ 49 $\approx$ 5

Where:

49 x 5 = 320

Finally, we have a Quotient generated after combining the three pieces of it as 0.765=z, with a Remainder equal to 40. Images/mathematical drawings are created with GeoGebra.