Question

How do you write $ 3.875 $ as a mixed number in simplest form?

Answer 1

Hint: Convert the given decimal number into fractional form first, then after converting it into fractional form, you will get an improper fraction, now convert that improper fraction into mixed number in simplest form.
Improper fraction $ \dfrac{a}{b} $ can be converted into mixed number as following:
 $ a \div b = cb + d $ , where “c” is the quotient and “d” is the remainder in the division then the mixed number is written as $ c\dfrac{d}{b} $

Complete step-by-step answer:
In order to write the given decimal number $ 3.875 $ as a mixed number, we have to convert the decimal number into fractional form first,
To convert a decimal into fraction we have to divide and multiply the decimal number by $ 10 $ raise to the power “n”, where “n” is the number of digits after the decimal.
So here in the given decimal number $ 3.875 $ the value of $ n = 3 $
Therefore dividing and multiplying $ 3.875\;{\text{with}}\;{10^n} = {10^3} = 1000 $
 $
   = \dfrac{{3.875 \times 1000}}{{1000}} \\
   = \dfrac{{3875}}{{1000}} \;
  $
Now we got the decimal number in fraction which is an improper one, to convert this improper fraction into mixed number dividing the numerator with denominator and noting the quotient and remainder
 $ \Rightarrow 3875 \div 1000 = 3 $ with a remainder of \[875\]
So we can write it in mixed form as
 $ = 3\dfrac{{875}}{{1000}} $
We have to simplify this further in order to make this mixed number in simplest form
So we will take out the common factor between numerator and denominator
 $
   = 3\dfrac{{875}}{{1000}} \\
   = 3\dfrac{{5 \times 5 \times 5 \times 7}}{{5 \times 5 \times 5 \times 2 \times 2 \times 2}} \;
  $
We can further write it as
 $
   = 3\dfrac{{5 \times 5 \times 5 \times 7}}{{5 \times 5 \times 5 \times 2 \times 2 \times 2}} \\
   = 3\dfrac{7}{{2 \times 2 \times 2}} \\
   = 3\dfrac{7}{8} \;
  $
So $ 3\dfrac{7}{8} $ is the simplest form of mixed number of $ 3.875 $
So, the correct answer is “ $ 3\dfrac{7}{8} $ ”.

Note: In this question we have terminating decimal, but there are non terminating decimals too which are a bit hard to convert into fractions, but there are some easy steps by which you can convert them into fractions.