71/7 as a Decimal and Mixed Number

71/7 as a decimal and mixed number expansion provides the detailed information about what is 71/7 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

71/7 as a Decimal Expansion
71/7 = 10.1429
Hence,
71/7 as a decimal equals to 10.1429
where,
71/7 is a given fraction,
The decimal expansion of 71/7 is 10.1429

71/7 as a Mixed Number
71/7 = (70 + 1)/7
= 70/7 + 1/7
= 10 + 1/7
= 10 1/7
71/7 = 10 1/7

Hence,
71/7 as a mixed number is 10 ¹/₇
where,
71/7 is a given fraction,
10 ¹/₇ is the mixed number representation of 71/7.

The below work with steps provide the detailed information about how to convert fraction 71/7 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 71/7

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 71/7.

step 2 The numerator is greater than the denominator of the fraction 71/7, so write the given fraction in the expression form in terms of denominator as like the below:
= 71/7
= 70 + 1/7
= (10 x 7) + 1/7

step 3 Make the above expression as individual fractions:
= (10 x 7)/7 + 1/7

step 4 Simplify the above expression:
= 10 x 7/7 + 1/7
= 10 + 1/7
10 + 1/7 can be written as a mixed number 10 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.
= 10 + (1/7 x 10/10)

step 6 Simplify the above expression further:
= 10 + (10/7 x 1/10)
= 10 + (7 + 3/7 x 1/10)
= 10 + [(7/7 + 3/7 ) x 1/10]
= 10 + [(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:
= 10 + [(1 + 3/7) x 1/10]
= 10 + [(1 + 0.43) x 1/10]
= 10 + (1.43 x 1/10)
= 10 + 1.43/10
= 10 + 0.143

step 8 Find the sum of above expression:
= 10 + 0.143
= 10.143
71/7 = 10.143

Hence,
71/7 as a decimal is 10.143
71/7 as a mixed number is 10 ¹/₇