Which one of the following is a whole number but not a natural number?
22
−12
3
0
−12
-12 is neither a whole number nor a natural number, so the correct answer was 0. good try tho
Apologies for the incorrect response. You are correct. -12 is neither a whole number nor a natural number. The correct answer is 0, which is a whole number but not a natural number. Thank you for pointing out the error.
Which set of numbers is the largest family group that includes all of the others?
real numbers
rational numbers
natural numbers
irrational numbers
The largest family group that includes all the other sets of numbers is the set of real numbers. The real numbers include all rational numbers, all natural numbers, and all irrational numbers.
Which numbers are both integers and irrational numbers?
square roots of integers
zero
none
negative integers
None of the numbers mentioned in the options are both integers and irrational numbers. Integers are rational numbers since they can be expressed as a fraction or a ratio of two integers. Irrational numbers, on the other hand, cannot be expressed as a fraction of two integers. Therefore, there are no numbers that are both integers and irrational numbers.
Which of the following may call for negative numbers?
lengths of time
street addresses
page numbers of a book
temperature measurements
Temperature measurements may call for negative numbers. Temperature can be measured on a scale where values below a certain point (such as 0 degrees Celsius or freezing point) are considered negative.
Which real-world problem is most likely to involve irrational numbers?
finding the diameter of a circle based on the radius
finding the total cost of filling up a car’s tank based on the price per gallon
finding the width of a rectangle based on the area and the length
finding the side length of a square based on the area
The real-world problem most likely to involve irrational numbers is finding the side length of a square based on the area. This is because the area of a square is given by multiplying the side length by itself. If the area involves an irrational number, such as when the area is the square root of a non-perfect square, then the side length of the square will also be an irrational number.
What kind of fraction is irrational?
a fraction with 0 in the numerator
a fraction with π as the numerator or denominator
an improper fraction
a fraction with a negative integer as the numerator
A fraction with π as the numerator or denominator is considered an irrational fraction. Irrational numbers cannot be expressed as a fraction of two integers, and π is an example of an irrational number.
Which of the following is rational?
1/√3 (1 over 3 square rooted in fraction)
√3/1 (3 square rooted over 1 in fraction)
√3 + √3 (3 square rooted plus 3 square rooted)
√3 × √3 (3 square rooted times 3 square rooted)
The rational number among the given options is √3 * √3 (the square root of 3 times the square root of 3). When multiplied, the square root of 3 multiplied by itself equals 3, which is a rational number. The other expressions involving square roots do not result in rational numbers.
Which is the best estimate for 3 times pi?
9 1/7 (9 and 1 over 7 as mixed number)
6 3/7 (6 and 3 over 7 as mixed number)
9 3/7 (9 and 3 over 7 as mixed number)
6 4/7 (6 and 4 over 7 as mixed number)
The best estimate for 3 times pi is 9 3/7 (9 and 3/7 as a mixed number).
Using a number line, what is the approximate value of √39?
6.25
6.42
6.33
6.17
To approximate the value of √39 on a number line, we can find the whole number closest to the square root of 39.
The square root of 39 is between 6 and 7, as 6^2 = 36 and 7^2 = 49.
Since 39 is closer to 36 than 49, the value of √39 is closer to 6 than 7.
Among the options provided, 6.25 is the closest approximation to the value of √39 on a number line.
Using rational approximations, what statement is true?
3 < √9
π > √9
π < √9
3 > √9
Using rational approximations, the true statement is 3 > √9.
The square root of 9 is 3, which is a rational number. Therefore, 3 is equal to √9 in this context.
it was actually pi was greater than √9
Apologies for the confusion. You are correct. Using rational approximations, the true statement is π > √9.
The rational approximation of π is 3.14, which is greater than the square root of 9, which is 3.
For a rational number to generate a repeating decimal, what must be true?
The denominator must be a prime number.
The numerator must be an odd number.
The rational number must not be a mixed number.
The denominator must not evenly divide any power of 10.
For a rational number to generate a repeating decimal, the denominator must not evenly divide any power of 10.
When a rational number is expressed as a fraction, the decimal representation is repeating if and only if the denominator contains prime factors other than 2 and 5. This means that the denominator must not evenly divide any power of 10, since 10 is equal to 2 multiplied by 5.
A repeating decimal can be converted to what kind of number?
an infinite decimal
an irrational number
a rational number
an integer
A repeating decimal can be converted to a rational number.
A repeating decimal is a decimal representation of a fraction where one or more digits repeat infinitely. It can be expressed as a quotient of two integers, making it a rational number.
When is it possible to find a rational number between two given rational numbers?
It is possible only when the difference between the two given numbers is at least 0.00001.
It is always possible to find a rational number between any two rational numbers.
It is possible only when the two given numbers are positive.
It is possible only when the two given numbers are integers.
It is always possible to find a rational number between any two rational numbers.
This is because between any two rational numbers, we can always find an infinite number of other rational numbers. We can take the average of the two given rational numbers as a rational number that lies between them. Therefore, regardless of the values or properties of the given rational numbers, it is always possible to find a rational number between them.