89/11 as a Decimal and Mixed Number

89/11 as a decimal and mixed number expansion provides the detailed information about what is 89/11 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

89/11 as a Decimal Expansion
89/11 = 8.0909
Hence,
89/11 as a decimal equals to 8.0909
where,
89/11 is a given fraction,
The decimal expansion of 89/11 is 8.0909

89/11 as a Mixed Number
89/11 = (88 + 1)/11
= 88/11 + 1/11
= 8 + 1/11
= 8 1/11
89/11 = 8 1/11

Hence,
89/11 as a mixed number is 8 ¹/₁₁
where,
89/11 is a given fraction,
8 ¹/₁₁ is the mixed number representation of 89/11.

The below work with steps provide the detailed information about how to convert fraction 89/11 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 89/11

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 89/11.

step 2 The numerator is greater than the denominator of the fraction 89/11, so write the given fraction in the expression form in terms of denominator as like the below:
= 89/11
= 88 + 1/11
= (8 x 11) + 1/11

step 3 Make the above expression as individual fractions:
= (8 x 11)/11 + 1/11

step 4 Simplify the above expression:
= 8 x 11/11 + 1/11
= 8 + 1/11
8 + 1/11 can be written as a mixed number 8 ¹/₁₁.


step 5 Find the decimal equivalent for the fractional part 1/11 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/11. Since the denominator is having 1 more digit than the numerator, multiply 100 with both numerator and denominator of 1/11.
= 8 + (1/11 x 100/100)

step 6 Simplify the above expression further:
= 8 + (100/11 x 1/100)
= 8 + (99 + 1/11 x 1/100)
= 8 + [(99/11 + 1/11 ) x 1/100]
= 8 + [(9 + 1/11) x 1/100]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 1/11 in the above expression:
= 8 + [(9 + 1/11) x 1/100]
= 8 + [(9 + 0.09) x 1/100]
= 8 + (9.09 x 1/100)
= 8 + 9.09/100
= 8 + 0.0909

step 8 Find the sum of above expression:
= 8 + 0.0909
= 8.0909
89/11 = 8.0909

Hence,
89/11 as a decimal is 8.0909
89/11 as a mixed number is 8 ¹/₁₁