47/13 as a Decimal and Mixed Number

47/13 as a decimal and mixed number expansion provides the detailed information about what is 47/13 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

47/13 as a Decimal Expansion
47/13 = 3.6154
Hence,
47/13 as a decimal equals to 3.6154
where,
47/13 is a given fraction,
The decimal expansion of 47/13 is 3.6154

47/13 as a Mixed Number
47/13 = (39 + 8)/13
= 39/13 + 8/13
= 3 + 8/13
= 3 8/13
47/13 = 3 8/13

Hence,
47/13 as a mixed number is 3 ⁸/₁₃
where,
47/13 is a given fraction,
3 ⁸/₁₃ is the mixed number representation of 47/13.

The below work with steps provide the detailed information about how to convert fraction 47/13 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 47/13

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 47/13.

step 2 The numerator is greater than the denominator of the fraction 47/13, so write the given fraction in the expression form in terms of denominator as like the below:
= 47/13
= 39 + 8/13
= (3 x 13) + 8/13

step 3 Make the above expression as individual fractions:
= (3 x 13)/13 + 8/13

step 4 Simplify the above expression:
= 3 x 13/13 + 8/13
= 3 + 8/13
3 + 8/13 can be written as a mixed number 3 ⁸/₁₃.


step 5 Find the decimal equivalent for the fractional part 8/13 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 8/13. Since the denominator is having 1 more digit than the numerator, multiply 100 with both numerator and denominator of 8/13.
= 3 + (8/13 x 100/100)

step 6 Simplify the above expression further:
= 3 + (800/13 x 1/100)
= 3 + (793 + 7/13 x 1/100)
= 3 + [(793/13 + 7/13 ) x 1/100]
= 3 + [(61 + 7/13) x 1/100]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 7/13 in the above expression:
= 3 + [(61 + 7/13) x 1/100]
= 3 + [(61 + 0.54) x 1/100]
= 3 + (61.54 x 1/100)
= 3 + 61.54/100
= 3 + 0.6154

step 8 Find the sum of above expression:
= 3 + 0.6154
= 3.6154
47/13 = 3.6154

Hence,
47/13 as a decimal is 3.6154
47/13 as a mixed number is 3 ⁸/₁₃