83/45 as a decimal and mixed number expansion provides the detailed information about what is 83/45 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.
83/45 as a Decimal Expansion
83/45 = 1.8444
Hence,
83/45 as a decimal equals to 1.8444
where,
83/45 is a given fraction,
The decimal expansion of 83/45 is 1.8444
83/45 as a Mixed Number
83/45 = (45 + 38)/45
= 45/45 + 38/45
= 1 + 38/45
= 1 38/45
83/45 = 1 38/45
Hence,
83/45 as a mixed number is 1 38/45
where,
83/45 is a given fraction,
1 38/45 is the mixed number representation of 83/45.
The below work with steps provide the detailed information about how to convert fraction 83/45 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 83/45
What to be found:
Find the equivalent decimal expansion and mixed number for fraction 83/45.
step 2 The numerator is greater than the denominator of the fraction 83/45, so write the given fraction in the expression form in terms of denominator as like the below:
= 83/45
= 45 + 38/45
step 3 Make the above expression as individual fractions:
= 45/45 + 38/45
step 4 Simplify the above expression:
= 1 x 45/45 + 38/45
= 1 + 38/45
1 + 38/45 can be written as a mixed number 1 38/45.
step 5 Find the decimal equivalent for the fractional part 38/45 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 38/45. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 38/45.
= 1 + (38/45 x 10/10)
step 6 Simplify the above expression further:
= 1 + (380/45 x 1/10)
= 1 + (360 + 20/45 x 1/10)
= 1 + [(360/45 + 20/45 ) x 1/10]
= 1 + [(8 + 20/45) x 1/10]
step 7 Repeat the step 5 to find the decimal equivalent for the fraction 20/45 in the above expression:
= 1 + [(8 + 20/45) x 1/10]
= 1 + [(8 + 0.44) x 1/10]
= 1 + (8.44 x 1/10)
= 1 + 8.44/10
= 1 + 0.844
step 8 Find the sum of above expression:
= 1 + 0.844
= 1.844
83/45 = 1.844
Hence,
83/45 as a decimal is 1.844
83/45 as a mixed number is 1 38/45