What Is 34/40 as a Decimal + Solution With Free Steps

The fraction 34/40 as a decimal is equal to 0.85.

The operation of division is notated p $\boldsymbol\div$ q can produce either integer or decimal values, depending on the values of the dividend p and the divisor q. Sometimes, it is useful to represent it in a more compact form of the numeral p/q. This alternate notation is called a fraction, where p is the numerator and q is the denominator.

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 34/40.

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 = 34

Divisor = 40

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 = 34 $\div$ 40

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

Figure 1

34/40 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 34 and 40, we can see how 34 is Smaller than 40, and to solve this division, we require that 34 be Bigger than 40.

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 34, which after getting multiplied by 10 becomes 340.

We take this 340 and divide it by 40; this can be done as follows:

340 $\div$ 40 $\approx$ 8

Where:

40 x 8 = 320

This will lead to the generation of a Remainder equal to 340 – 320 = 20. Now this means we have to repeat the process by Converting the 20 into 200 and solving for that:

200 $\div$ 40 = 5

Where:

40 x 5 = 200

This, therefore, produces another Remainder which is equal to 200 – 200 = 0. The division is complete, so we have the Quotient as 0.85 with a final remainder of 0.

Images/mathematical drawings are created with GeoGebra.