Find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
Find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, you need to convert 2 1/4 to an improper fraction.
2 1/4 = (2 * 4 + 1) / 4 = 9/4
Now, add 2 and 9/4 together:
2 + 9/4 = 8/4 + 9/4 = 17/4
Next, divide 17/4 by 2:
(17/4) ÷ 2 = 17/4 ÷ 2/1 = 17/4 * 1/2 = (17*1) / (4*2) = 17/8
Therefore, the rational number between 2 and 2 1/4 using the given method is 17/8.
As a mixed number, this can be written as 2 1/8.
Find a rational number with one decimal place that is between 17−−√ and 18−−√.(1 point)
To find a rational number with one decimal place that is between √17 and √18, we can approximate the square roots as follows:
√17 ≈ 4.123
√18 ≈ 4.243
Now, we can find a rational number between these two approximation by taking their average and rounding to one decimal place:
(4.123 + 4.243) / 2 ≈ 4.183
Therefore, a rational number with one decimal place between √17 and √18 is approximately 4.2.
Show an example of an irrational number between 9 and 11.(1 point)
Responses
99−−√
square root of 99
20−−√
square root of 20
10−−√
square root of 10
100−−−√
square root of 100
An example of an irrational number between 9 and 11 is √10 (the square root of 10). The value of √10 is approximately 3.16.
Which of the following is an irrational number between 7 and 10?(1 point)
Responses
To identify an irrational number between 7 and 10, we can check the given options:
- square root of 49
- square root of 64
- square root of 81
- square root of 100
The square root of 49 is 7, which is not an irrational number.
The square root of 64 is 8, which is also not an irrational number.
The square root of 81 is 9, which is still not an irrational number.
The square root of 100 is 10, which is not an irrational number either.
Therefore, none of the given options represents an irrational number between 7 and 10.
Which of the following is an irrational number between 7 and 10?(1 point)
Responses
8–√
square root of 8
55−−√
square root of 55
64−−√
square root of 64
81−−√
To find an irrational number between 7 and 10, we can check the given options:
- √8 (square root of 8)
- √55 (square root of 55)
- √64 (square root of 64)
- √81 (square root of 81)
The square root of 8 is approximately 2.828, which is an irrational number.
The square root of 55 is approximately 7.416, which is also an irrational number.
The square root of 64 is 8, which is not an irrational number.
The square root of 81 is 9, which is not an irrational number.
Therefore, the irrational numbers between 7 and 10 are √8 and √55.