What Is 7/90 as a Decimal + Solution With Free Steps

The fraction 7/90 as a decimal is equal to 0.077777.

Fractions are expressed as p/q, where q≠0, while decimals are written as the whole number part connected with the fractional part by a decimal point like 0.7. Interestingly, a fraction can be readily converted to its decimal form for which the most commonly used method is “Long Division“.

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.

7 90 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 7/90.


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 = 7

Divisor = 90

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 = 7 $\div$ 90

This is when we go through the Long Division solution to our problem. The following shows the long division:

7/90 Long Division Method

Figure 1

7/90 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 7 and 90, we can see how 7 is Smaller than 90, and to solve this division, we require that 7 be Bigger than 90.

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 7, which after getting multiplied by 10 twice and adding zero in Quotient after the decimal point becomes 700.

We take this 700 and divide it by 90; this can be done as follows:

 700 $\div$ 90 $\approx$ 7


90 x 7 = 630

This will lead to the generation of a Remainder equal to 700 – 630 = 70. Now this means we have to repeat the process by Converting the 70 into 700 and solving for that:

700 $\div$ 90 $\approx$ 7 


90 x 7 = 630

This, therefore, produces another Remainder equal to 700 – 630 = 70. Now we stop solving this problem, we have a Quotient generated after combining the three pieces of it as 0.077=z, with a Remainder equal to 70.

7 by 90 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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