Which set of numbers is always irrational?(1 point)
Responses
non-terminating, non-repeating decimals
non-terminating, non-repeating decimals
positive decimals
positive decimals
repeating decimals
repeating decimals
terminating decimals
non-terminating, non-repeating decimals
The diagonal of a square equals 2–√
times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 70 feet on a side?(1 point)
To find the length from one corner to an opposite corner of a square park, we can use the formula:
diagonal length = (2–√) * side length
Given that the side length is 70 feet, we can substitute this value into the formula:
diagonal length = (2–√) * 70
Substituting the approximate value 1.4 for the square root of 2:
diagonal length ≈ (2–1.4) * 70
diagonal length ≈ 0.6 * 70
diagonal length ≈ 42 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 42 feet.
Four people have found the distance in kilometers across a small bridge using different methods. Their results are given in the table. Order the distances from least to greatest.
A. 5 1/2, 28, 5.5, 23/4
B. 28, 5 1/2, 5.5, 23/4
C. 28, 5.5, 23/4, 5 1/2
D. 23/4, 5.5, 28, 5 1/2
To order the distances from least to greatest, we need to convert all the distances into the same format.
Let's convert 5 1/2 to its decimal form. 5 1/2 is equal to 5.5.
Now, let's convert 23/4 to its decimal form. To do this, we divide 23 by 4, resulting in 5.75.
Now that all the distances are in decimal form, we can order them from least to greatest:
5.5, 5.75, 28
Therefore, the correct order is:
C. 28, 5.5, 23/4, 5 1/2
Using a number line, what whole number and rational number to the nearest half is 30 between? (1 point)
30 is between blank and blank
To determine the whole number and rational number to the nearest half that 30 is between, we can locate 30 on a number line:
0-------------------30-------------------60
We can see that 30 is exactly halfway between the whole numbers 0 and 60. However, since the question asks for the nearest half, we need to consider the rational numbers in increments of 0.5.
If we divide the space between 0 and 60 into increments of 0.5, we can determine the rational number to the nearest half that 30 is between:
0, 0.5, 1, 1.5, ... 28, 28.5, 29, 29.5, 30, 30.5, 31, 31.5, ..., 59, 59.5, 60
Therefore, the whole number and rational number to the nearest half that 30 is between is:
29 and 30.5
Using a number line, what whole number and rational to the nearest half is 68 between?
A. between 9 and 9.5
B. between 8.5 and 9
C. between 7.5 and 8
D. between 8 and 8.5
To determine the whole number and rational number to the nearest half that 68 is between, we can locate 68 on a number line:
0----------------------------68---------------------------100
We can see that 68 is closer to 68.5 than any other option given. Therefore, the correct answer is:
A. between 9 and 9.5
Using rational approximations, what is an inequality statement comparing 91 and 98? Enter greater, less, or equal
The inequality is: 91 blank 98
The inequality between 91 and 98 is:
91 < 98
Therefore, the inequality statement is:
91 < 98
Express 7/11 as a repeating decimal. Mark the cycle of repeating digits with a bar. Note: You will find the option to add a bar above text in the geometry keyboard.
To express 7/11 as a repeating decimal, we perform long division:
0.636363...
We obtained a repeating pattern of "36", so we can write 7/11 as 0.63 with a bar above the digits 63:
7/11 = 0.63 ̅
Convert 0.09 to a rational number in simplest form
To convert the decimal 0.09 to a rational number in simplest form, we can express it as a fraction by placing the decimal value over a power of 10.
0.09 can be written as 9/100 because the decimal is two places after the decimal point, and 100 is 10 raised to the power of 2.
Therefore, 0.09 in simplest form as a rational number is 9/100.
Convert 0.7 to a fraction
The fraction equivalent of 0,7 is blank
To convert 0.7 to a fraction, we can write it as 7/10.
Therefore, the fraction equivalent of 0.7 is 7/10.
Which of the following is an irrational number between 4 and 8?
A. 12
B. 8
C. 5
D. 17
To determine which of the given options is an irrational number between 4 and 8, we need to understand the properties of irrational numbers.
An irrational number is a number that cannot be expressed as a fraction or a terminating or repeating decimal.
Based on this definition, the only option that can potentially be an irrational number is:
D. 17
To confirm whether 17 is irrational, we need to check if it can be expressed as a fraction or a terminating or repeating decimal.
Since 17 is an integer and can be expressed as 17/1, it is a rational number, not an irrational number.
Therefore, none of the given options is an irrational number between 4 and 8.
Which of the following rational numbers is not between 3 and 6?
A. 1.8
B. 4
C. 1.5
D. 2
To determine which of the given rational numbers is not between 3 and 6, we can compare them to the given range.
A. 1.8 is less than 3 and not between 3 and 6.
B. 4 is between 3 and 6.
C. 1.5 is less than 3 and not between 3 and 6.
D. 2 is between 3 and 6.
Therefore, the rational number that is not between 3 and 6 is:
A. 1.8
Describe the relationship between integers and whole numbers. Are all integers also whole numbers? Are all whole numbers also integers? Give examples to support your answer.
The relationship between integers and whole numbers is that all integers are also whole numbers, but not all whole numbers are integers.
Integers include both positive and negative whole numbers, as well as zero. Examples of integers are -3, -2, -1, 0, 1, 2, and 3.
On the other hand, whole numbers include only positive whole numbers and zero, meaning they do not include negative numbers. Examples of whole numbers are 0, 1, 2, and 3.
Therefore, all integers are also whole numbers because they include all the positive and negative whole numbers. However, not all whole numbers are integers since integers include the negative numbers as well.
In summary:
- Integers include all positive and negative whole numbers and zero.
- Whole numbers include only positive whole numbers and zero.
Examples:
-2 is an integer and also a whole number.
2 is an integer and also a whole number.
5 is a whole number but not an integer.
0 is both an integer and a whole number.