81/40 as a decimal and mixed number expansion provides the detailed information about what is 81/40 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.
81/40 as a Decimal Expansion
81/40 = 2.025
Hence,
81/40 as a decimal equals to 2.025
where,
81/40 is a given fraction,
The decimal expansion of 81/40 is 2.025
81/40 as a Mixed Number
81/40 = (80 + 1)/40
= 80/40 + 1/40
= 2 + 1/40
= 2 1/40
81/40 = 2 1/40
Hence,
81/40 as a mixed number is 2 1/40
where,
81/40 is a given fraction,
2 1/40 is the mixed number representation of 81/40.
The below work with steps provide the detailed information about how to convert fraction 81/40 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 81/40
What to be found:
Find the equivalent decimal expansion and mixed number for fraction 81/40.
step 2 The numerator is greater than the denominator of the fraction 81/40, so write the given fraction in the expression form in terms of denominator as like the below:
= 81/40
= 80 + 1/40
= (2 x 40) + 1/40
step 3 Make the above expression as individual fractions:
= (2 x 40)/40 + 1/40
step 4 Simplify the above expression:
= 2 x 40/40 + 1/40
= 2 + 1/40
2 + 1/40 can be written as a mixed number 2 1/40.
step 5 Find the decimal equivalent for the fractional part 1/40 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/40. Since the denominator is having 1 more digit than the numerator, multiply 100 with both numerator and denominator of 1/40.
= 2 + (1/40 x 100/100)
step 6 Simplify the above expression further:
= 2 + (100/40 x 1/100)
= 2 + (80 + 20/40 x 1/100)
= 2 + [(80/40 + 20/40 ) x 1/100]
= 2 + [(2 + 20/40) x 1/100]
step 7 Repeat the step 5 to find the decimal equivalent for the fraction 20/40 in the above expression:
= 2 + [(2 + 20/40) x 1/100]
= 2 + [(2 + 0.5) x 1/100]
= 2 + (2.5 x 1/100)
= 2 + 2.5/100
= 2 + 0.025
step 8 Find the sum of above expression:
= 2 + 0.025
= 2.025
81/40 = 2.025
Hence,
81/40 as a decimal is 2.025
81/40 as a mixed number is 2 1/40