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What Is 4/75 as a Decimal + Solution With Free Steps

The fraction 4/75 as a decimal is equal to 0.053.

The decimal form and the fractional form are interchangeable. We know that Division is one of the four primary operators of mathematics therefore by applying the long division method the fraction can be converted to its equivalent decimal. When the long division is performed on the fraction 4/75 it results in its equivalent recurring decimal.

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 4/75.

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 = 4

Divisor = 75

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 = 4 $\div$ 75

This is when we go through the Long Division solution to our problem. The solution for fraction 4/75 is given in the figure below.

4/75 Long Division Method

Figure 1

4/75 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 4 and 75, we can see how 4 is Smaller than 75, and to solve this division, we require that 4 be Bigger than 75.

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.

Since 4 when multiplied by 10 becomes 40 which is still smaller than 75. Therefore we will multiply 40 by 10 again and add a zero in the quotient after the decimal point. By doing this the dividend will become 400 which is bigger than 75 and hence divisible by 75.

Now, we begin solving for our dividend 400.

We take this 400 and divide it by 75; this can be done as follows:

 400 $\div$ 75 $\approx$ 5

Where:

75 x 5 = 375

This will lead to the generation of a Remainder equal to 400 – 375 = 25. Now this means we have to repeat the process by Converting the 25 into 250 and solving for that:

250 $\div$ 75 $\approx$ 3

Where:

75 x 3 = 225

Finally, we have a Quotient generated after combining the three pieces of it as 0.053, with a Remainder equal to 25.

4_75 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra. 

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