What Is 6/75 as a Decimal + Solution With Free Steps

The fraction 6/75 as a decimal is equal to 0.08.

Fractions involve division, and division seems the most difficult one among all mathematical operators, but actually it is not that much tougher because we have a way to deal with the problem. To make them easier to understand, we convert fractions to decimal values.

Here, we are interested more in the types of division that results 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 75 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 6/75.


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 seen done as follows:

Dividend = 6

Divisor = 75

Now, we introduce the most important quantity in our process of division, this is 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 $\div$ 75

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

6/75 Long Division Method

Figure 1

6/75 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 75 we can see how 6 is Smaller than 75, and to solve this division we require that 6 be Bigger than 75.

This is done by multiplying the dividend by 10 and checking whether it is bigger than the divisor or not. And if it is then we calculate the Multiple of the divisor which is 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 6, which after getting multiplied by 10 becomes 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.

We take this 600 and divide it by 75, this can be seen done as follows:

 600 $\div$ 75 = 8


75 x 8 = 600

This will lead to the generation of a Remainder equal to 600 – 600 = 0.

So, we have a Quotient of 0.8 = z, with a Remainder equal to 0.

6 by 75 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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