89/8 as a Decimal and Mixed Number

89/8 as a decimal and mixed number expansion provides the detailed information about what is 89/8 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

89/8 as a Decimal Expansion
89/8 = 11.125
Hence,
89/8 as a decimal equals to 11.125
where,
89/8 is a given fraction,
The decimal expansion of 89/8 is 11.125

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

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

The below work with steps provide the detailed information about how to convert fraction 89/8 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 89/8

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 89/8.

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

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

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


step 5 Find the decimal equivalent for the fractional part 1/8 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/8. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 1/8.
= 11 + (1/8 x 10/10)

step 6 Simplify the above expression further:
= 11 + (10/8 x 1/10)
= 11 + (8 + 2/8 x 1/10)
= 11 + [(8/8 + 2/8 ) x 1/10]
= 11 + [(1 + 2/8) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 2/8 in the above expression:
= 11 + [(1 + 2/8) x 1/10]
= 11 + [(1 + 0.25) x 1/10]
= 11 + (1.25 x 1/10)
= 11 + 1.25/10
= 11 + 0.125

step 8 Find the sum of above expression:
= 11 + 0.125
= 11.125
89/8 = 11.125

Hence,
89/8 as a decimal is 11.125
89/8 as a mixed number is 11 ¹/₈