1) Which of these is a rational number?
a. Pi
b. Square root 3 ******
c. Square root 2
d. 1.3 (the # 3 has a line at the top)
2) Which of the following sets contains 3 irrational numbers?
a. Square root 120 , n , Square root 3 ******
b. - Square root 256 , 1/9 , 1/12
c. 3.14 , -47 , 100
d. n , Square root 0.36 , Square root 121
1.
π --- irrational
√3 --- irrational
√2 --- irrational
1.333.... = 4/3 ---- Rational
2. If n is your symbol for π
then your choice if a) is correct
1) The rational number is:
b. Square root 3
2) The set containing 3 irrational numbers is:
a. Square root 120, n, Square root 3
To determine whether a number is rational or irrational, we need to understand the definition of each.
1) Rational numbers:
- Rational numbers can be expressed as fractions, where both the numerator and denominator are integers.
- They can be written in decimal form, which can either terminate (example: 0.5) or repeat in a pattern (example: 0.333...).
2) Irrational numbers:
- Irrational numbers cannot be expressed as fractions and have decimal representations that do not terminate or repeat.
- Examples of irrational numbers include square roots of non-perfect squares (√2, √3), or numbers like pi (π) that have an infinite number of non-repeating decimal digits.
Now, let's analyze the given options:
1) Which of these is a rational number?
- Option a: Pi (π) is an irrational number, as it cannot be expressed as a fraction and has a non-repeating decimal representation.
- Option b: The square root of 3 (√3) is also an irrational number, as it cannot be expressed as a fraction and has a non-repeating decimal representation.
- Option c: The square root of 2 (√2) is another example of an irrational number.
- Option d: The number 1.3 (with a line on top) is a rational number. This is because the line indicates that the decimal representation terminates after one digit (1.3) and can be expressed as a fraction (13/10).
Therefore, the correct answer is d. 1.3 (the number with a line on top).
2) Which of the following sets contains 3 irrational numbers?
- Option a: This set contains the square root of 120 (√120), which is irrational since it cannot be expressed as a fraction. It also contains the square root of 3 (√3), which is irrational. Therefore, this set contains two irrational numbers: √120 and √3.
- Option b: This set contains the square root of 256 (√256), which is rational because it can be simplified to 16 (a perfect square). It does not contain any irrational numbers.
- Option c: This set contains only rational numbers (3.14, -47, 100).
- Option d: This set contains the square root of 0.36 (√0.36), which is rational because it can be simplified to 0.6 (a terminating decimal). It also contains the square root of 121 (√121), which is rational since it simplifies to 11 (a perfect square). Therefore, this set contains two rational numbers and one irrational number (√0.36).
Therefore, the correct answer is a. Square root 120, n, Square root 3 as it contains three irrational numbers: √120, n, and √3.