write the decimal expansion of i) ⅐ ii) ⅓
Answers
For example, consider the number 33.33333……. It is a rational number as it can be represented in the form of 100/3. It can be seen that the decimal part .333…… is the non-terminating repeating part, i .e. it is a recurring decimal number.
Also the terminating decimals such as 0.375, 0.6 etc. which satisfy the condition of being rational (0.375 = 323 ,0.6 = 35).
Consider any decimal number. For e.g. 0.567. It can be written as 567/1000 or 567103 . Similarly, the numbers 0.6689,0.032 and .45 can be written as 6689104 ,32103 and 45102 respectively in fractional form.
Thus, it can be seen that any decimal number can be represented as a fraction which has denominator in powers of 10. We know that prime factors of 10 are 2 and 5, it can be concluded that any decimal rational number can be easily represented in the form of pq, such that p and q are integers and the prime factorization of q is of the form 2x 5y, where x and y are non-negative integers.
This statement gives rise to a very important theorem.
Answer:
decimal expansion of 1/7 is 0.1428...
decimal expansion of 1/3 is 0.33....