23/3 as a Decimal and Mixed Number

23/3 as a decimal and mixed number expansion provides the detailed information about what is 23/3 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

23/3 as a Decimal Expansion
23/3 = 7.6667
Hence,
23/3 as a decimal equals to 7.6667
where,
23/3 is a given fraction,
The decimal expansion of 23/3 is 7.6667

23/3 as a Mixed Number
23/3 = (21 + 2)/3
= 21/3 + 2/3
= 7 + 2/3
= 7 2/3
23/3 = 7 2/3

Hence,
23/3 as a mixed number is 7 ²/₃
where,
23/3 is a given fraction,
7 ²/₃ is the mixed number representation of 23/3.

The below work with steps provide the detailed information about how to convert fraction 23/3 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 23/3

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 23/3.

step 2 The numerator is greater than the denominator of the fraction 23/3, so write the given fraction in the expression form in terms of denominator as like the below:
= 23/3
= 21 + 2/3
= (7 x 3) + 2/3

step 3 Make the above expression as individual fractions:
= (7 x 3)/3 + 2/3

step 4 Simplify the above expression:
= 7 x 3/3 + 2/3
= 7 + 2/3
7 + 2/3 can be written as a mixed number 7 ²/₃.


step 5 Find the decimal equivalent for the fractional part 2/3 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 2/3. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 2/3.
= 7 + (2/3 x 10/10)

step 6 Simplify the above expression further:
= 7 + (20/3 x 1/10)
= 7 + (18 + 2/3 x 1/10)
= 7 + [(18/3 + 2/3 ) x 1/10]
= 7 + [(6 + 2/3) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 2/3 in the above expression:
= 7 + [(6 + 2/3) x 1/10]
= 7 + [(6 + 0.67) x 1/10]
= 7 + (6.67 x 1/10)
= 7 + 6.67/10
= 7 + 0.667

step 8 Find the sum of above expression:
= 7 + 0.667
= 7.667
23/3 = 7.667

Hence,
23/3 as a decimal is 7.667
23/3 as a mixed number is 7 ²/₃