40/13 as a Decimal and Mixed Number
40/13 as a decimal and mixed number expansion provides the detailed information about what is 40/13 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.
40/13 as a Decimal Expansion
40/13 = 3.0769
Hence,
40/13 as a decimal equals to 3.0769
where,
40/13 is a given fraction,
The decimal expansion of 40/13 is 3.0769
40/13 as a Mixed Number
40/13 = (39 + 1)/13
= 39/13 + 1/13
= 3 + 1/13
= 3 1/13
40/13 = 3 1/13
Hence,
40/13 as a mixed number is 3 1/13
where,
40/13 is a given fraction,
3 1/13 is the mixed number representation of 40/13.
How-to: 40/13 as a Decimal
The below work with steps provide the detailed information about how to convert fraction 40/13 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 40/13
What to be found:
Find the equivalent decimal expansion and mixed number for fraction 40/13.
step 2 The numerator is greater than the denominator of the fraction 40/13, so write the given fraction in the expression form in terms of denominator as like the below:
= 40/13
= 39 + 1/13
= (3 x 13) + 1/13
step 3 Make the above expression as individual fractions:
= (3 x 13)/13 + 1/13
step 4 Simplify the above expression:
= 3 x 13/13 + 1/13
= 3 + 1/13
3 + 1/13 can be written as a mixed number 3 1/13.
step 5 Find the decimal equivalent for the fractional part 1/13 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/13. Since the denominator is having 1 more digit than the numerator, multiply 100 with both numerator and denominator of 1/13.
= 3 + (1/13 x 100/100)
step 6 Simplify the above expression further:
= 3 + (100/13 x 1/100)
= 3 + (91 + 9/13 x 1/100)
= 3 + [(91/13 + 9/13 ) x 1/100]
= 3 + [(7 + 9/13) x 1/100]
step 7 Repeat the step 5 to find the decimal equivalent for the fraction 9/13 in the above expression:
= 3 + [(7 + 9/13) x 1/100]
= 3 + [(7 + 0.69) x 1/100]
= 3 + (7.69 x 1/100)
= 3 + 7.69/100
= 3 + 0.0769
step 8 Find the sum of above expression:
= 3 + 0.0769
= 3.0769
40/13 = 3.0769
Hence,
40/13 as a decimal is 3.0769
40/13 as a mixed number is 3 1/13