26/9 as a Decimal and Mixed Number

The below work with steps provide the detailed information about how to convert fraction 26/9 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 26/9

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 26/9.

step 2 The numerator is greater than the denominator of the fraction 26/9, so write the given fraction in the expression form in terms of denominator as like the below:
= 26/9
= 18 + 8/9
= (2 x 9) + 8/9

step 3 Make the above expression as individual fractions:
= (2 x 9)/9 + 8/9

step 4 Simplify the above expression:
= 2 x 9/9 + 8/9
= 2 + 8/9
2 + 8/9 can be written as a mixed number 2 ⁸/₉.


step 5 Find the decimal equivalent for the fractional part 8/9 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 8/9. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 8/9.
= 2 + (8/9 x 10/10)

step 6 Simplify the above expression further:
= 2 + (80/9 x 1/10)
= 2 + (72 + 8/9 x 1/10)
= 2 + [(72/9 + 8/9 ) x 1/10]
= 2 + [(8 + 8/9) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 8/9 in the above expression:
= 2 + [(8 + 8/9) x 1/10]
= 2 + [(8 + 0.89) x 1/10]
= 2 + (8.89 x 1/10)
= 2 + 8.89/10
= 2 + 0.889

step 8 Find the sum of above expression:
= 2 + 0.889
= 2.889
26/9 = 2.889

Hence,
26/9 as a decimal is 2.889
26/9 as a mixed number is 2 ⁸/₉