What Is 3 7/8 as a Decimal + Solution With Free Steps

The fraction 3 7/8 as a decimal is equal to 3.875.

The given fraction is known as a mixed fraction. Mixed fractions are those having both a whole number and an improper fraction. Fractions have three types: improper fraction, proper fraction, and mixed fraction. When the numerator of the fraction is greater than the denominator, it is known as an improper fraction.

Similarly, a fraction having a numerator less than the denominator is referred to as a proper fraction.

Here we have to convert the given mixed fraction of 3 7/8 into a decimal value. To convert a fraction into a decimal value, we need to divide. And division seems to be one of the most difficult operations in mathematical problems, but there is a way to deal with this. The method we use to solve the fraction is the Long Division method.

Solution

First, we will convert the given mixed fraction into an improper fraction. For that, we will multiply the whole number with the denominator, then add the numerator to it. So the given mixed fraction of 3 7/8 is equivalent to 31/8.

Dividend-specified terms are necessary to introduce before starting the solution, and the terms are Dividend and Divisor. The dividend is the fraction’s numerator, and the divisor is its denominator.

Dividend = 31

Divisor = 8

Here we will introduce a new term which is the result of the fraction in decimal value and is known as the Quotient.

Quotient = Dividend $ \div $ Divisor = 31 $ \div $ 8

The solution by using the long division method is as under:

Figure 1

3 7/8 Long Division Method

We can solve the fraction by the method called long division:

31 $ \div $ 8

Here we have a case of a greater numerator than the denominator, so we can directly divide both the numbers.

Here is a new term to be introduced. When we have two numbers that are not exactly divisible by each other, the remaining number after their division is known as the Remainder.

31 $ \div $ 8 $ \approx $ 3

Where:

 8 x 3 = 24

We have a remainder of 7.

So now here is the case of a remainder less than the divisor, so we have to multiply our remainder by ten. For that, we will add the decimal point to the quotient.

So now we have a remainder of 70.

70 $ \div $ 8 $ \approx $ 8

Where:

 8 x 8 = 64

After this step, we have a remainder of 6, so by multiplying our remainder again with ten, we end up having a remainder of 60:

60 $ \div $ 8 $ \approx $ 7

Where:

 8 x 7 = 56

So the resulting Quotient of the given mixed fraction of 3 7/8 is 3.87 with the Remainder of 4. To get a more precise answer, we can solve it further.

Images/mathematical drawings are created with GeoGebra.

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