100/99 as a decimal and mixed number expansion provides the detailed information about what is 100/99 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.
100/99 as a Decimal Expansion
100/99 = 1.0101
Hence,
100/99 as a decimal equals to 1.0101
where,
100/99 is a given fraction,
The decimal expansion of 100/99 is 1.0101
100/99 as a Mixed Number
100/99 = (99 + 1)/99
= 99/99 + 1/99
= 1 + 1/99
= 1 1/99
100/99 = 1 1/99
Hence,
100/99 as a mixed number is 1 1/99
where,
100/99 is a given fraction,
1 1/99 is the mixed number representation of 100/99.
The below work with steps provide the detailed information about how to convert fraction 100/99 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 100/99
What to be found:
Find the equivalent decimal expansion and mixed number for fraction 100/99.
step 2 The numerator is greater than the denominator of the fraction 100/99, so write the given fraction in the expression form in terms of denominator as like the below:
= 100/99
= 99 + 1/99
step 3 Make the above expression as individual fractions:
= 99/99 + 1/99
step 4 Simplify the above expression:
= 1 + 1/99
1 + 1/99 can be written as a mixed number 1 1/99
step 5 Find the decimal equivalent for the fractional part 1/99 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/99. Since the denominator is having 1 more digit than the numerator, multiply 100 with both numerator and denominator of 1/99.
= 1 + (1/99 x 100/100)
step 6 Simplify the above expression further:
= 1 + (100/99 x 1/100)
= 1 + (99 + 1/99 x 1/100)
= 1 + [(99/99 + 1/99 ) x 1/100]
= 1 + [(1 + 1/99) x 1/100]
step 7 Repeat the step 5 to find the decimal equivalent for the fraction 1/99 in the above expression:
= 1 + [(1 + 1/99) x 1/100]
= 1 + [(1 + 0.01) x 1/100]
= 1 + (1.01 x 1/100)
= 1 + 1.01/100
= 1 + 0.0101
step 8 Find the sum of above expression:
= 1 + 0.0101
= 1.0101
100/99 = 1.0101
Hence,
100/99 as a decimal is 1.0101
100/99 as a mixed number is 1 1/99