47/8 as a Decimal and Mixed Number

47/8 as a decimal and mixed number expansion provides the detailed information about what is 47/8 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

47/8 as a Decimal Expansion
47/8 = 5.875
Hence,
47/8 as a decimal equals to 5.875
where,
47/8 is a given fraction,
The decimal expansion of 47/8 is 5.875

47/8 as a Mixed Number
47/8 = (40 + 7)/8
= 40/8 + 7/8
= 5 + 7/8
= 5 7/8
47/8 = 5 7/8

Hence,
47/8 as a mixed number is 5 ⁷/₈
where,
47/8 is a given fraction,
5 ⁷/₈ is the mixed number representation of 47/8.

The below work with steps provide the detailed information about how to convert fraction 47/8 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 47/8

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 47/8.

step 2 The numerator is greater than the denominator of the fraction 47/8, so write the given fraction in the expression form in terms of denominator as like the below:
= 47/8
= 40 + 7/8
= (5 x 8) + 7/8

step 3 Make the above expression as individual fractions:
= (5 x 8)/8 + 7/8

step 4 Simplify the above expression:
= 5 x 8/8 + 7/8
= 5 + 7/8
5 + 7/8 can be written as a mixed number 5 ⁷/₈.


step 5 Find the decimal equivalent for the fractional part 7/8 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 7/8. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 7/8.
= 5 + (7/8 x 10/10)

step 6 Simplify the above expression further:
= 5 + (70/8 x 1/10)
= 5 + (64 + 6/8 x 1/10)
= 5 + [(64/8 + 6/8 ) x 1/10]
= 5 + [(8 + 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:
= 5 + [(8 + 6/8) x 1/10]
= 5 + [(8 + 0.75) x 1/10]
= 5 + (8.75 x 1/10)
= 5 + 8.75/10
= 5 + 0.875

step 8 Find the sum of above expression:
= 5 + 0.875
= 5.875
47/8 = 5.875

Hence,
47/8 as a decimal is 5.875
47/8 as a mixed number is 5 ⁷/₈