205/208 as a Decimal

205/208 as a decimal expansion provides the detailed information about what is 205/208 in decimal form, and the answer with steps help students to easily understand how it is being calculated.

205/208 as a Decimal
205/208 = 0.9856
Hence,
205/208 as a decimal equals to 0.9856
where,
205/208 is a given fraction,
The decimal expansion of 205/208 is 0.9856

205/208 as a Mixed Number
The given fraction 205/208 can't be represented as a mixed number since the numerator 205 of the given fraction is smaller than the denominator 208.

The below work with steps provide the detailed information about how to convert fraction 205/208 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 205/208

What to be found:
Find the decimal expansion of fraction 205/208.

step 2 The numerator is smaller than the denominator of the fraction 205/208, so find how many 10s should be multiplied with both numerator and denominator. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 205/208.
= 205/208 x 10/10

step 3 Rearrange the fraction as like the below:
= 10 x 205/208 x 1/10
= 2050/208 x 1/10

step 4 Simplify the above expression further:
= 2050/208 x 1/10
= 1872 + 178/208 x 1/10
= ( 1872/208 + 178/208) x 1/10
= (9 + 178/208 ) x 1/10

step 5 Repeat the step 2 to find the decimal equivalent for the fraction 178/208 in the above expression:
= (9 + 178/208 ) x 1/10
= (9 + 0.856) x 1/10

step 6 Simplify the above expression further:
= (9 + 0.856) x 1/10
= 9.856 x 1/10
= 9.856/10
205/208= 0.9856

Hence,
205/208 as a decimal is 0.9856