012. ) Express the rational number 1/11 in decimal form and hence find the
decimal expansion of 47/11
(11) Express the rational number 1/13 a decimal form and hence find the
decimal expansion of 3/13, 4:13 and 5/13.
Answers
Answer:
Step-by-step explanation:
1/11 = 0.090909090909090909........................
47/11 = 4.272727272727272727....................
1/13 = 0.076923076923...............................
MARK AS BRAINLIEST
Answer:
1/11 = 0.09090909....(non terminating recurring decimal)
47/11 = 4.272727.......(non terminating recurring decimal)
1/13 = 0.0769230769....... (non terminating non recurring decimal)
3/13 = 0.230769231..............(non terminating non recurring decimal)
4/13 = 0.307692308............(non terminating non recurring decimal)
5/13 = 0.384615385...............(non terminating non recurring decimal)
Step-by-step explanation:
When the numerator of a rational number is divided by its denominator, we get the decimal expansion of the rational number. The decimal numbers thus obtained can be of two types.
Terminating decimals
Non-terminating decimals
1. Terminating Decimal Numbers
The decimal numbers having finite numbers of digits after the decimal point are known as the terminating decimal numbers. Their number of decimal places is finite. These decimal numbers are called exact decimal numbers. We can represent these decimal numbers in p/q form where q≠0.
2. Non-Terminating Decimal Numbers
The decimal numbers having infinite numbers of digits after the decimal point are known as the non-terminating decimal numbers.
- Recurring Decimals
The decimal numbers having infinite numbers of digits after the decimal point, and the digits are repeated at equal intervals after the decimal point are known as the recurring decimal numbers.
- Non-recurring Decimals
The decimal numbers having infinite numbers of digits after the decimal point and the digits not repeated at equal intervals after the decimal point are known as the non-recurring decimal numbers.
Note: The property that q must satisfy to be a terminating decimal in the form of p/q (q ≠ 0), where p and q are integers with no common factors other than 1 is that q must be in the form of 2^a × 5^b where a and b are whole numbers.
1/11 = 0.09090909....(non terminating recurring decimal) Rational Number
47/11 = 4.272727.......(non-terminating recurring decimal) Rational Number
1/13 = 0.0769230769....... (non terminating non recurring decimal) Irrational Number
3/13 = 0.230769231..............(non terminating non recurring decimal)
Irrational Number
4/13 = 0.307692308............(non terminating non recurring decimal)
Irrational Number
5/13 = 0.384615385...............(non terminating non recurring decimal)
Irrational Number
