22/7 as a Decimal and Mixed Number

The below work with steps provide the detailed information about how to convert fraction 22/7 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 22/7

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 22/7.

step 2 The numerator is greater than the denominator of the fraction 22/7, so write the given fraction in the expression form in terms of denominator as like the below:
= 22/7
= 21 + 1/7
= (3 x 7) + 1/7

step 3 Make the above expression as individual fractions:
= (3 x 7)/7 + 1/7

step 4 Simplify the above expression:
= 3 x 7/7 + 1/7
= 3 + 1/7
3 + 1/7 can be written as a mixed number 3 ¹/₇.


step 5 Find the decimal equivalent for the fractional part 1/7 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/7. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 1/7.
= 3 + (1/7 x 10/10)

step 6 Simplify the above expression further:
= 3 + (10/7 x 1/10)
= 3 + (7 + 3/7 x 1/10)
= 3 + [(7/7 + 3/7 ) x 1/10]
= 3 + [(1 + 3/7) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 3/7 in the above expression:
= 3 + [(1 + 3/7) x 1/10]
= 3 + [(1 + 0.43) x 1/10]
= 3 + (1.43 x 1/10)
= 3 + 1.43/10
= 3 + 0.143

step 8 Find the sum of above expression:
= 3 + 0.143
= 3.143
22/7 = 3.143

Hence,
22/7 as a decimal is 3.143
22/7 as a mixed number is 3 ¹/₇