31/9 as a Decimal and Mixed Number

31/9 as a decimal and mixed number expansion provides the detailed information about what is 31/9 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

31/9 as a Decimal Expansion
31/9 = 3.4444
Hence,
31/9 as a decimal equals to 3.4444
where,
31/9 is a given fraction,
The decimal expansion of 31/9 is 3.4444

31/9 as a Mixed Number
31/9 = (27 + 4)/9
= 27/9 + 4/9
= 3 + 4/9
= 3 4/9
31/9 = 3 4/9

Hence,
31/9 as a mixed number is 3 ⁴/₉
where,
31/9 is a given fraction,
3 ⁴/₉ is the mixed number representation of 31/9.

The below work with steps provide the detailed information about how to convert fraction 31/9 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 31/9

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 31/9.

step 2 The numerator is greater than the denominator of the fraction 31/9, so write the given fraction in the expression form in terms of denominator as like the below:
= 31/9
= 27 + 4/9
= (3 x 9) + 4/9

step 3 Make the above expression as individual fractions:
= (3 x 9)/9 + 4/9

step 4 Simplify the above expression:
= 3 x 9/9 + 4/9
= 3 + 4/9
3 + 4/9 can be written as a mixed number 3 ⁴/₉.


step 5 Find the decimal equivalent for the fractional part 4/9 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 4/9. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 4/9.
= 3 + (4/9 x 10/10)

step 6 Simplify the above expression further:
= 3 + (40/9 x 1/10)
= 3 + (36 + 4/9 x 1/10)
= 3 + [(36/9 + 4/9 ) x 1/10]
= 3 + [(4 + 4/9) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 4/9 in the above expression:
= 3 + [(4 + 4/9) x 1/10]
= 3 + [(4 + 0.44) x 1/10]
= 3 + (4.44 x 1/10)
= 3 + 4.44/10
= 3 + 0.444

step 8 Find the sum of above expression:
= 3 + 0.444
= 3.444
31/9 = 3.444

Hence,
31/9 as a decimal is 3.444
31/9 as a mixed number is 3 ⁴/₉