77/9 as a Decimal and Mixed Number

77/9 as a decimal and mixed number expansion provides the detailed information about what is 77/9 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

77/9 as a Decimal Expansion
77/9 = 8.5556
Hence,
77/9 as a decimal equals to 8.5556
where,
77/9 is a given fraction,
The decimal expansion of 77/9 is 8.5556

77/9 as a Mixed Number
77/9 = (72 + 5)/9
= 72/9 + 5/9
= 8 + 5/9
= 8 5/9
77/9 = 8 5/9

Hence,
77/9 as a mixed number is 8 ⁵/₉
where,
77/9 is a given fraction,
8 ⁵/₉ is the mixed number representation of 77/9.

The below work with steps provide the detailed information about how to convert fraction 77/9 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 77/9

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 77/9.

step 2 The numerator is greater than the denominator of the fraction 77/9, so write the given fraction in the expression form in terms of denominator as like the below:
= 77/9
= 72 + 5/9
= (8 x 9) + 5/9

step 3 Make the above expression as individual fractions:
= (8 x 9)/9 + 5/9

step 4 Simplify the above expression:
= 8 x 9/9 + 5/9
= 8 + 5/9
8 + 5/9 can be written as a mixed number 8 ⁵/₉.


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

step 6 Simplify the above expression further:
= 8 + (50/9 x 1/10)
= 8 + (45 + 5/9 x 1/10)
= 8 + [(45/9 + 5/9 ) x 1/10]
= 8 + [(5 + 5/9) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 5/9 in the above expression:
= 8 + [(5 + 5/9) x 1/10]
= 8 + [(5 + 0.56) x 1/10]
= 8 + (5.56 x 1/10)
= 8 + 5.56/10
= 8 + 0.556

step 8 Find the sum of above expression:
= 8 + 0.556
= 8.556
77/9 = 8.556

Hence,
77/9 as a decimal is 8.556
77/9 as a mixed number is 8 ⁵/₉