1. Which of the following is an irrational number: 25−−√, π, or 0/27? HELP ASAP I CAN'T FAIL THE REAL NUMBER SYSTEM PRACTICE
An irrational number is a number that cannot be expressed as a fraction or a decimal that terminates or repeats.
Out of the options given:
1. √25 - This is a rational number because it equals 5, which can be expressed as the fraction 5/1.
2. π - This is an irrational number because it cannot be expressed as a terminating decimal or a repeating decimal. It is a never-ending, non-repeating decimal.
3. 0/27 - This is a rational number because it equals 0, which can be expressed as the fraction 0/1.
Therefore, the irrational number among the options given is π.
Of the following numbers, which is an integer but does not belong in either of the subsets of integers: −13, 0, or 13?
The subsets of integers are the positive integers (including zero) and the negative integers.
Given the numbers:
1. −13 - This is a negative integer and belongs to the subset of negative integers.
2. 0 - This is an integer and belongs to both the subset of positive integers (including zero) and the subset of negative integers.
3. 13 - This is a positive integer and belongs to the subset of positive integers (including zero).
Therefore, the number that is an integer but does not belong in either of the subsets of integers is 0.
Which of the following is an integer but not a whole number: 0, −2, 7, 783?
An integer is a number that can be positive, negative, or zero, without any decimal or fractional parts.
A whole number is a number that is non-negative and has no fractional or decimal part. It includes positive integers and zero.
Given the numbers:
1. 0 - This is an integer and a whole number because it is non-negative and has no fractional or decimal part.
2. -2 - This is an integer but not a whole number because it is negative.
3. 7 - This is an integer and a whole number because it is non-negative and has no fractional or decimal part.
4. 783 - This is an integer and a whole number because it is non-negative and has no fractional or decimal part.
Therefore, the number that is an integer but not a whole number is -2.
Four square gardens have the following areas in square meters: 144, 32, 72, and 250. Which area has a rational number of meters as the side length?
To determine which area corresponds to a rational number as the side length of the square, we need to see if the square root of the area is a rational number.
Given the areas:
1. 144 - The square root of 144 is 12, which is a rational number.
2. 32 - The square root of 32 is approximately 5.656854249..., which is an irrational number.
3. 72 - The square root of 72 is approximately 8.485281374..., which is an irrational number.
4. 250 - The square root of 250 is approximately 15.811388300..., which is an irrational number.
Therefore, the area that corresponds to a rational number as the side length of the square is 144.
You want to calculate the circumference of a circular skating pond by multiplying the diameter times pi. Which of the following values of pi will give the most accurate answer: 3.14, 3.14159, 22/7, or 3.1416?
To calculate the circumference of a circular skating pond, the most accurate value of pi should be used.
Out of the options given:
1. 3.14 - This is an approximation of pi that is commonly used, but it is not as accurate as some other representations.
2. 3.14159 - This is a more accurate approximation of π as it includes more decimal places.
3. 22/7 - This is another approximation of pi commonly used, but it is not as accurate as the actual value of pi.
4. 3.1416 - This is another approximation of pi that includes more decimal places, making it more accurate than 3.14 but not as accurate as 3.14159.
Therefore, the value of pi that will give the most accurate answer for the circumference is 3.14159.
To determine which of the given numbers is irrational, let's first understand what an irrational number is. An irrational number is a number that cannot be expressed as a fraction or ratio of two integers. It cannot be written as a terminating or repeating decimal. Now, let's check each option:
1. √25: This is the square root of 25, which equals 5. Since 5 can be expressed as a ratio of integers (5/1), it is a rational number.
2. π (pi): Pi is approximately 3.14159 and is a non-repeating, non-terminating decimal. It cannot be expressed as a fraction of two integers, so it is an irrational number.
3. 0/27: Any number divided by zero is undefined. In this case, 0 divided by any number, including 27, is 0. Since 0 can be expressed as a ratio of two integers (0/1), it is a rational number.
Therefore, the irrational number among the options provided is π, option 2.