Solved Questions of Decimal Expansion of Rational Numbers
1. Which of the following is a rational number?
a) 0.367239623962...
b) 0.93754432
c) 1.414213562373...
d) √7
Answer: b) 0.93754432
Explanation: The decimal expansion of a rational number terminates or repeats after a finite number of decimal places. Option b) has a terminating decimal expansion, which means it is a rational number.
The other options have non-terminating or non-repeating decimal expansions, which are irrational numbers.
2. The decimal expansion of the rational number 5/8 is?
a) 0.625
b) 0.6666...
c) 0.5555...
d) 0.70710678118...
Answer: a) 0.625
Explanation: To convert a fraction into a decimal, divide the numerator by the denominator. So, 5/8 = 0.625
Therefore, the decimal expansion of the rational number 5/8 is 0.625.
3. Which of the following is a rational number?
a) 0.12856325632...
b) 3.1415926535...
c) 0.166666666...
d) √11
Answer: c) 0.166666666...
Explanation: The decimal expansion of a rational number terminates or repeats after a finite number of decimal places. Option c) has a repeating decimal expansion, which means it is a rational number.
The other options have non-terminating or non-repeating decimal expansions, which are irrational numbers.
4. Which of the following is a rational number?
a) √3
b) √10
c) √16
d) √23
Answer: c) √16
Explanation: A rational number can be expressed as a fraction of two integers, and the square root of a perfect square is an integer.
Therefore, √16 = 4, which is an integer and can be expressed as a fraction of two integers. The other options have non-terminating or non-repeating decimal expansions, which are irrational numbers.
5. Which of the following fractions has a non-terminating but repeating decimal expansion?
a) 5/7
b) 4/5
c) 3/8
d) 2/3
Answer: a) 5/7
Explanation: To convert a fraction into a decimal, divide the numerator by the denominator. So, 5/7 = 0.714285... The decimal expansion of 5/7 is non-terminating, but it repeats after a certain number of decimal places.
Therefore, it is a non-terminating but repeating decimal.
Worksheet of Decimal Expansion of Rational Numbers
1. What is the repeating decimal equivalent of the rational number 1/7?
a) 0.42857142857...
b) 0.142857142857...
c) 0.171428571428...
d) 0.71428571428...
Answer: b) 0.142857142857...
2. Which of the following is a terminating decimal?
a) 0.5
b) 0.666666...
c) 0.83……
d) 0.25……
Answer: a) 0.5
3. What is the fraction equivalent of the repeating decimal 2.3333333...
a) 21/9
b) 1/3
c) 2/7
d) 5/16
Answer: a) 21/9
4. Which of the following is NOT a terminating decimal?
a) 0.625
b) 0.25
c) 0.375
d) 0.33……
Answer: d) 0.33…...
6. What is the decimal representation of 3/11?
a) 0.272727….
b) 0.4285714….
c) 0.265343...
d) 0.428571….
Answer: a) 0.272727…...
7. What is the decimal representation of 1/3?
a) 0.32323232
b) 0.33333……
c) 0.111111
d) 1.3333333….
Answer: b) 0.33333……
8. What is the decimal representation of 1/9?
a) 0.11111….
b) 0.13131….
c) 0.11211….
d) 0.12121….
Answer: a) 0.11111…...
9. What is the decimal representation of 2/5?
a) 0.45
b) 0.25
c) 0.41
d) 0.40
Answer: d) 0.40
10. Which of the following is a rational number?
a) 0.12856325632...
b) 3.1415926535...
c) 0.166666666...
d) √11
Answer: c) 0.166666666...
