89/9 as a Decimal and Mixed Number

89/9 as a decimal and mixed number expansion provides the detailed information about what is 89/9 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

89/9 as a Decimal Expansion
89/9 = 9.8889
Hence,
89/9 as a decimal equals to 9.8889
where,
89/9 is a given fraction,
The decimal expansion of 89/9 is 9.8889

89/9 as a Mixed Number
89/9 = (81 + 8)/9
= 81/9 + 8/9
= 9 + 8/9
= 9 8/9
89/9 = 9 8/9

Hence,
89/9 as a mixed number is 9 ⁸/₉
where,
89/9 is a given fraction,
9 ⁸/₉ is the mixed number representation of 89/9.

The below work with steps provide the detailed information about how to convert fraction 89/9 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 89/9

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 89/9.

step 2 The numerator is greater than the denominator of the fraction 89/9, so write the given fraction in the expression form in terms of denominator as like the below:
= 89/9
= 81 + 8/9
= (9 x 9) + 8/9

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

step 4 Simplify the above expression:
= 9 x 9/9 + 8/9
= 9 + 8/9
9 + 8/9 can be written as a mixed number 9 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.
= 9 + (8/9 x 10/10)

step 6 Simplify the above expression further:
= 9 + (80/9 x 1/10)
= 9 + (72 + 8/9 x 1/10)
= 9 + [(72/9 + 8/9 ) x 1/10]
= 9 + [(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:
= 9 + [(8 + 8/9) x 1/10]
= 9 + [(8 + 0.89) x 1/10]
= 9 + (8.89 x 1/10)
= 9 + 8.89/10
= 9 + 0.889

step 8 Find the sum of above expression:
= 9 + 0.889
= 9.889
89/9 = 9.889

Hence,
89/9 as a decimal is 9.889
89/9 as a mixed number is 9 ⁸/₉