29/9 as a Decimal and Mixed Number

The below work with steps provide the detailed information about how to convert fraction 29/9 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 29/9

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 29/9.

step 2 The numerator is greater than the denominator of the fraction 29/9, so write the given fraction in the expression form in terms of denominator as like the below:
= 29/9
= 27 + 2/9
= (3 x 9) + 2/9

step 3 Make the above expression as individual fractions:
= (3 x 9)/9 + 2/9

step 4 Simplify the above expression:
= 3 x 9/9 + 2/9
= 3 + 2/9
3 + 2/9 can be written as a mixed number 3 ²/₉.


step 5 Find the decimal equivalent for the fractional part 2/9 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 2/9. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 2/9.
= 3 + (2/9 x 10/10)

step 6 Simplify the above expression further:
= 3 + (20/9 x 1/10)
= 3 + (18 + 2/9 x 1/10)
= 3 + [(18/9 + 2/9 ) x 1/10]
= 3 + [(2 + 2/9) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 2/9 in the above expression:
= 3 + [(2 + 2/9) x 1/10]
= 3 + [(2 + 0.22) x 1/10]
= 3 + (2.22 x 1/10)
= 3 + 2.22/10
= 3 + 0.222

step 8 Find the sum of above expression:
= 3 + 0.222
= 3.222
29/9 = 3.222

Hence,
29/9 as a decimal is 3.222
29/9 as a mixed number is 3 ²/₉