82/9 as a Decimal and Mixed Number

82/9 as a decimal and mixed number expansion provides the detailed information about what is 82/9 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

82/9 as a Decimal Expansion
82/9 = 9.1111
Hence,
82/9 as a decimal equals to 9.1111
where,
82/9 is a given fraction,
The decimal expansion of 82/9 is 9.1111

82/9 as a Mixed Number
82/9 = (81 + 1)/9
= 81/9 + 1/9
= 9 + 1/9
= 9 1/9
82/9 = 9 1/9

Hence,
82/9 as a mixed number is 9 ¹/₉
where,
82/9 is a given fraction,
9 ¹/₉ is the mixed number representation of 82/9.

The below work with steps provide the detailed information about how to convert fraction 82/9 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 82/9

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 82/9.

step 2 The numerator is greater than the denominator of the fraction 82/9, so write the given fraction in the expression form in terms of denominator as like the below:
= 82/9
= 81 + 1/9
= (9 x 9) + 1/9

step 3 Make the above expression as individual fractions:
= (9 x 9)/9 + 1/9

step 4 Simplify the above expression:
= 9 x 9/9 + 1/9
= 9 + 1/9
9 + 1/9 can be written as a mixed number 9 ¹/₉.


step 5 Find the decimal equivalent for the fractional part 1/9 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/9. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 1/9.
= 9 + (1/9 x 10/10)

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

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 1/9 in the above expression:
= 9 + [(1 + 1/9) x 1/10]
= 9 + [(1 + 0.11) x 1/10]
= 9 + (1.11 x 1/10)
= 9 + 1.11/10
= 9 + 0.111

step 8 Find the sum of above expression:
= 9 + 0.111
= 9.111
82/9 = 9.111

Hence,
82/9 as a decimal is 9.111
82/9 as a mixed number is 9 ¹/₉