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
5) Which is equivalent to the expression shown? 5^-3
a. -125
b. -15
c. 1/125 *****
d. 2
1)
1.3 = 13/10, so rational
or
1.333333...... = 1 1/3 = 4/3 which is rational
2)agree
3) agree
The answer for #1 is A Pi = )
Who's right?
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how many irrational numbers are between the square root of 11 and square root of 17?
To determine if a number is rational or irrational, we need to understand their definitions.
A rational number can be expressed as the quotient or fraction of two integers, where the denominator is not zero. On the other hand, an irrational number cannot be expressed as a simple fraction and has an infinite, non-repeating decimal representation.
1) To determine which of the given options is a rational number, let's examine each option:
a. Pi: Pi is an irrational number since it cannot be expressed as a simple fraction and has a decimal representation that goes on forever without repeating.
b. Square root 3: The square root of 3 is also an irrational number. It cannot be expressed as a simple fraction, and its decimal representation is an infinite non-repeating decimal.
c. Square root 2: The square root of 2 is another irrational number. It cannot be expressed as a simple fraction, and its decimal representation is also an infinite non-repeating decimal.
d. 1.3 (the number 3 has a line at the top): This number is a rational number since it can be expressed as the fraction 13/10. The line indicates that the 3 is recurring.
Therefore, option b. Square root 3 is an irrational number.
2) To find which set contains three irrational numbers:
A. Square root 120, n, Square root 3: This set contains two irrational numbers: square root 120 and square root 3.
B. - Square root 256, 1/9, 1/12: None of these numbers are irrational. Square root 256 is a rational number because it equals 16. 1/9 and 1/12 are also rational numbers since they can be expressed as fractions.
C. 3.14, -47, 100: None of these numbers are irrational. 3.14 is a rational number since it can be expressed as 314/100. -47 and 100 are also rational numbers because they can be expressed as whole numbers.
D. n, Square root 0.36, Square root 121: This set contains only one irrational number: square root 0.36.
Therefore, option A. Square root 120, n, Square root 3 contains three irrational numbers.
3) To determine the equivalence of the expression 5^-3:
This expression can be rewritten as 1/5^3.
5^3 means 5 multiplied by itself three times: 5 x 5 x 5 = 125.
Therefore, 5^-3 is equal to 1/125.
Therefore, option c. 1/125 is equivalent to the expression 5^-3.