42/13 as a Decimal and Mixed Number

42/13 as a decimal and mixed number expansion provides the detailed information about what is 42/13 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

42/13 as a Decimal Expansion
42/13 = 3.2308
Hence,
42/13 as a decimal equals to 3.2308
where,
42/13 is a given fraction,
The decimal expansion of 42/13 is 3.2308

42/13 as a Mixed Number
42/13 = (39 + 3)/13
= 39/13 + 3/13
= 3 + 3/13
= 3 3/13
42/13 = 3 3/13

Hence,
42/13 as a mixed number is 3 ³/₁₃
where,
42/13 is a given fraction,
3 ³/₁₃ is the mixed number representation of 42/13.

The below work with steps provide the detailed information about how to convert fraction 42/13 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 42/13

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 42/13.

step 2 The numerator is greater than the denominator of the fraction 42/13, so write the given fraction in the expression form in terms of denominator as like the below:
= 42/13
= 39 + 3/13
= (3 x 13) + 3/13

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

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


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

step 6 Simplify the above expression further:
= 3 + (300/13 x 1/100)
= 3 + (299 + 1/13 x 1/100)
= 3 + [(299/13 + 1/13 ) x 1/100]
= 3 + [(23 + 1/13) x 1/100]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 1/13 in the above expression:
= 3 + [(23 + 1/13) x 1/100]
= 3 + [(23 + 0.08) x 1/100]
= 3 + (23.08 x 1/100)
= 3 + 23.08/100
= 3 + 0.2308

step 8 Find the sum of above expression:
= 3 + 0.2308
= 3.2308
42/13 = 3.2308

Hence,
42/13 as a decimal is 3.2308
42/13 as a mixed number is 3 ³/₁₃