205/80 as a Decimal and Mixed Number

205/80 as a decimal and mixed number expansion provides the detailed information about what is 205/80 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

205/80 as a Decimal
205/80 = 2.5625
Hence,
205/80 as a decimal equals to 2.5625
where,
205/80 is a given fraction,
The decimal expansion of 205/80 is 2.5625

205/80 as a Mixed Number
205/80 = (160 + 45)/80
= 160/80 + 45/80
= 2 + 45/80
= 2 45/80
205/80 = 2 45/80

Hence,
205/80 as a mixed number is 2 ⁴⁵/₈₀
where,
205/80 is a given fraction,
2 ⁴⁵/₈₀ is the mixed number representation of 205/80.

The below work with steps provide the detailed information about how to convert fraction 205/80 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 205/80

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 205/80.

step 2 The numerator is greater than the denominator of the fraction 205/80, so write the given fraction in the expression form in terms of denominator as like the below:
= 205/80
= 160 + 45/80
= (2 x 80) + 45/80

step 3 Make the above expression as individual fractions:
= (2 x 80)/80 + 45/80

step 4 Simplify the above expression:
= 2 x 80/80 + 45/80
= 2 + 45/80
= 2 + 9 x 5/16 x 5
= 2 + 9/16
2 + 9/16 can be written as a mixed number 2 ⁹/₁₆.


step 5 Find the decimal equivalent for the fractional part 9/16 in the above expression:
Multiply both numerator and denominator by 625 to make the denominator as powers of 10:
= 2 + (9/16 x 625/625)
= 2 + 5625/10000

step 6 Simplify the above expression further:
= 2 + 0.5625
= 2.5625
205/80 = 2.5625

Hence,
205/80 as a decimal is 2.5625
205/80 as a mixed number is 2 ⁹/₁₆