The numbers that show decimal numbers that repeat indefinitely are called repeating decimals. For these numbers, we can determine fractions correspondents, which are called generating fractions.
A generating fraction can be found for both a simple repeating decimal and a repeating decimal. compound or mixed periodic, which is when the decimal has some decimals that are not repeated in addition to those that are repeat.
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To understand more about this subject, see a list of solved exercises on generating fraction.
Question 1. Calculate the generating fraction of each of the simple repeating decimals:
a) 3.21212121…
b) 1.888888…
c) 0.26262626…
d) 12.33333…
e) 17.89898989…
Question 2. Calculate the generating fraction of each of the compound repeating decimals:
a) 1.133333….
b) 3.563636363…
c) 17.415151515…
d) 0.244444…
e) 5.01209209209…
Question 3. Find the generating fraction to perform the following operations between decimal numbers:
a) 1.1212121212… + 1.17
b) 23.012121212… + 1.14141414…
Question 4. Using a generating fraction, find the result of the following operation:
3. (1,0131313… – 0, 0141414…)
Question 5. Using a generating fraction, find the result of the following operation:
0,54 + 3/5 – 1,22222… + 1,133333…
Even exact decimal numbers, that is, which are not repeating decimals, can be written as a fraction with the denominator being a multiple of 10.
So first let's write each of the decimal numbers as a fraction and then calculate the least common multiple to carry out the sum of fractions.
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