A mixed recurring decimal is a repeating decimal in which one or maybe more digits after the decimal point do not repeat, but the remaining digits or set of digits (after the decimal point) do.
It can be supported by citing some relevant cases, such as:
77/600 = 0.1283333333……. (Where 3 repeats up to infinity, but 128 doesn’t)
Conversion of Mixed Recurring Decimal:
The following steps can be used to convert mixed recurring decimals to a fraction:
Step 1: First, make a mixed recurring decimal number by eliminating the top bars, and then equate it to any variable x.
Step 2: Determine which digits following the decimal do not include a bar or are recurring.
Step 3: Multiply either side by 10b, where b is a non-recurring decimal number, and the equation is the result (i).
Step 4: At least two times, write a repeating decimal.
Step 5: If the n-digits have a bar, multiply both sides by 10n, and get equation (ii).
Step 6: Subtract equation (i) from (ii)
Step 7: Finally, divide either side of the equation by the x coefficient.
An example of how to convert mixed recurring decimal to fraction can be used to justify the preceding steps:
Suppose, x = 0.2555…
10x = 2.555… -equation (i)
10 x 10x = 10 x 2.555…
100x = 25.55… -equation (ii)
Subtracting equation (i) from equation (ii)
100x – 10x = 25.55… – 2.555…
90x = 23
x = 23/90
Hence, the value of 0.2555 (which is a mixed recurring decimal) is 23/90 (which is a vulgar fraction).
