8/3 as a Decimal and Mixed Number

The below work with steps provide the detailed information about how to convert fraction 8/3 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 8/3

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 8/3.

step 2 The numerator is greater than the denominator of the fraction 8/3, so write the given fraction in the expression form in terms of denominator as like the below:
= 8/3
= 6 + 2/3
= (2 x 3) + 2/3

step 3 Make the above expression as individual fractions:
= (2 x 3)/3 + 2/3

step 4 Simplify the above expression:
= 2 x 3/3 + 2/3
= 2 + 2/3
2 + 2/3 can be written as a mixed number 2 ²/₃.


step 5 Find the decimal equivalent for the fractional part 2/3 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 2/3. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 2/3.
= 2 + (2/3 x 10/10)

step 6 Simplify the above expression further:
= 2 + (20/3 x 1/10)
= 2 + (18 + 2/3 x 1/10)
= 2 + [(18/3 + 2/3 ) x 1/10]
= 2 + [(6 + 2/3) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 2/3 in the above expression:
= 2 + [(6 + 2/3) x 1/10]
= 2 + [(6 + 0.67) x 1/10]
= 2 + (6.67 x 1/10)
= 2 + 6.67/10
= 2 + 0.667

step 8 Find the sum of above expression:
= 2 + 0.667
= 2.667
8/3 = 2.667

Hence,
8/3 as a decimal is 2.667
8/3 as a mixed number is 2 ²/₃