What Is 65/72 as a Decimal + Solution With Free Steps

The fraction 65/72 as a decimal is equal to 0.902.

The division of two numbers is sometimes compactly represented in the form of a fraction, which is a numeral of the form p/q. Mathematically, a fraction can be evaluated the same way as the division, p $\boldsymbol\div$ q, where p and q are the dividend and divisor respectively.

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 65/72.

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 = 65

Divisor = 72

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 = 65 $\div$ 72

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

Figure 1

65/72 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 65 and 72, we can see how 65 is Smaller than 72, and to solve this division, we require that 65 be Bigger than 72.

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 65, which after getting multiplied by 10 becomes 650.

We take this 650 and divide it by 72; this can be done as follows:

650 $\div$ 72 $\approx$ 9

Where:

72 x 9 = 648

This will lead to the generation of a Remainder equal to 650 – 648 = 2. Now this means we have to repeat the process by Converting the 2 into 200. Since 2 x 10 = 20 is smaller than 72, we need to again multiply by 10. To indicate this second multiplication, we add a 0 to our quotient. Solving for that:

200 $\div$ 72 $\approx$ 2

Where:

72 x 2 = 144

Finally, we have a Quotient generated after combining the three pieces of it as 0.902, with a Remainder equal to 56.

Images/mathematical drawings are created with GeoGebra.