13/6 as a Decimal and Mixed Number

The below work with steps provide the detailed information about how to convert fraction 13/6 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 13/6

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 13/6.

step 2 The numerator is greater than the denominator of the fraction 13/6, so write the given fraction in the expression form in terms of denominator as like the below:
= 13/6
= 12 + 1/6
= (2 x 6) + 1/6

step 3 Make the above expression as individual fractions:
= (2 x 6)/6 + 1/6

step 4 Simplify the above expression:
= 2 x 6/6 + 1/6
= 2 + 1/6
2 + 1/6 can be written as a mixed number 2 ¹/₆.


step 5 Find the decimal equivalent for the fractional part 1/6 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/6. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 1/6.
= 2 + (1/6 x 10/10)

step 6 Simplify the above expression further:
= 2 + (10/6 x 1/10)
= 2 + (6 + 4/6 x 1/10)
= 2 + [(6/6 + 4/6 ) x 1/10]
= 2 + [(1 + 4/6) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 4/6 in the above expression:
= 2 + [(1 + 4/6) x 1/10]
= 2 + [(1 + 0.67) x 1/10]
= 2 + (1.67 x 1/10)
= 2 + 1.67/10
= 2 + 0.167

step 8 Find the sum of above expression:
= 2 + 0.167
= 2.167
13/6 = 2.167

Hence,
13/6 as a decimal is 2.167
13/6 as a mixed number is 2 ¹/₆