83/8 as a Decimal and Mixed Number

83/8 as a decimal and mixed number expansion provides the detailed information about what is 83/8 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

83/8 as a Decimal Expansion
83/8 = 10.375
Hence,
83/8 as a decimal equals to 10.375
where,
83/8 is a given fraction,
The decimal expansion of 83/8 is 10.375

83/8 as a Mixed Number
83/8 = (80 + 3)/8
= 80/8 + 3/8
= 10 + 3/8
= 10 3/8
83/8 = 10 3/8

Hence,
83/8 as a mixed number is 10 ³/₈
where,
83/8 is a given fraction,
10 ³/₈ is the mixed number representation of 83/8.

The below work with steps provide the detailed information about how to convert fraction 83/8 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 83/8

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 83/8.

step 2 The numerator is greater than the denominator of the fraction 83/8, so write the given fraction in the expression form in terms of denominator as like the below:
= 83/8
= 80 + 3/8
= (10 x 8) + 3/8

step 3 Make the above expression as individual fractions:
= (10 x 8)/8 + 3/8

step 4 Simplify the above expression:
= 10 x 8/8 + 3/8
= 10 + 3/8
10 + 3/8 can be written as a mixed number 10 ³/₈.


step 5 Find the decimal equivalent for the fractional part 3/8 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 3/8. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 3/8.
= 10 + (3/8 x 10/10)

step 6 Simplify the above expression further:
= 10 + (30/8 x 1/10)
= 10 + (24 + 6/8 x 1/10)
= 10 + [(24/8 + 6/8 ) x 1/10]
= 10 + [(3 + 6/8) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 6/8 in the above expression:
= 10 + [(3 + 6/8) x 1/10]
= 10 + [(3 + 0.75) x 1/10]
= 10 + (3.75 x 1/10)
= 10 + 3.75/10
= 10 + 0.375

step 8 Find the sum of above expression:
= 10 + 0.375
= 10.375
83/8 = 10.375

Hence,
83/8 as a decimal is 10.375
83/8 as a mixed number is 10 ³/₈