37/11 as a Decimal and Mixed Number

37/11 as a decimal and mixed number expansion provides the detailed information about what is 37/11 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

37/11 as a Decimal Expansion
37/11 = 3.3636
Hence,
37/11 as a decimal equals to 3.3636
where,
37/11 is a given fraction,
The decimal expansion of 37/11 is 3.3636

37/11 as a Mixed Number
37/11 = (33 + 4)/11
= 33/11 + 4/11
= 3 + 4/11
= 3 4/11
37/11 = 3 4/11

Hence,
37/11 as a mixed number is 3 ⁴/₁₁
where,
37/11 is a given fraction,
3 ⁴/₁₁ is the mixed number representation of 37/11.

The below work with steps provide the detailed information about how to convert fraction 37/11 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 37/11

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 37/11.

step 2 The numerator is greater than the denominator of the fraction 37/11, so write the given fraction in the expression form in terms of denominator as like the below:
= 37/11
= 33 + 4/11
= (3 x 11) + 4/11

step 3 Make the above expression as individual fractions:
= (3 x 11)/11 + 4/11

step 4 Simplify the above expression:
= 3 x 11/11 + 4/11
= 3 + 4/11
3 + 4/11 can be written as a mixed number 3 ⁴/₁₁.


step 5 Find the decimal equivalent for the fractional part 4/11 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 4/11. Since the denominator is having 1 more digit than the numerator, multiply 100 with both numerator and denominator of 4/11.
= 3 + (4/11 x 100/100)

step 6 Simplify the above expression further:
= 3 + (400/11 x 1/100)
= 3 + (396 + 4/11 x 1/100)
= 3 + [(396/11 + 4/11 ) x 1/100]
= 3 + [(36 + 4/11) x 1/100]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 4/11 in the above expression:
= 3 + [(36 + 4/11) x 1/100]
= 3 + [(36 + 0.36) x 1/100]
= 3 + (36.36 x 1/100)
= 3 + 36.36/100
= 3 + 0.3636

step 8 Find the sum of above expression:
= 3 + 0.3636
= 3.3636
37/11 = 3.3636

Hence,
37/11 as a decimal is 3.3636
37/11 as a mixed number is 3 ⁴/₁₁