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What Is 3/34 as a Decimal + Solution With Free Steps

The fraction 3/34 as a decimal is equal to 0.088.

The fraction 3/34 is a proper fraction because the numerator is less than the denominator. By applying the division method we can obtain decimal representation. Decimal notation is an alternative method for representing rational numbers.

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 3/34.

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 = 3

Divisor = 34

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 = 3 $\div$ 34

This is when we go through the Long Division solution to our problem. The following figure shows the solution for fraction 3/34.

3/34 Long Division Method

Figure 1

3/34 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 3 and 34, we can see how 3 is Smaller than 34, and to solve this division, we require that 3 be Bigger than 34.

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.

After multiplying the dividend 3 by 10, we get 30 which is smaller than 34. That means division is not possible. So to make it bigger than 34, the 30 is again multiplied by 10 which gives us 300. This is done by putting a zero in the quotient after the decimal point.

Now, we begin solving for our dividend 300.

We take this 300 and divide it by 34; this can be done as follows:

300$\div$ 34 $\approx$ 8

Where:

34 x 8 = 272

This will lead to the generation of a Remainder equal to 300 – 272 = 28. Now this means we have to repeat the process by Converting the 28 into 280 and solving for that:

280 $\div$ 34 $\approx$ 8

Where:

34 x 8 = 272

Finally, we have a Quotient generated after combining the three pieces of it as 0.088, with a Remainder equal to 8.

Images/mathematical drawings are created with GeoGebra.

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