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.(
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we first add the two numbers:
2 + 214 = 216
Then, we divide this sum by 2:
216 / 2 = 108
So, the rational number between 2 and 214 obtained by this method is 108.
Writing it as a mixed number, we can express it as:
108 = 100 + 8 = 100 + 8/1 = 100 8/1
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.(
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, we first convert 2 1/4 into an improper fraction.
2 1/4 = 9/4
Next, we add the two numbers:
2 + 9/4 = 8/4 + 9/4 = 17/4
Then, we divide this sum by 2:
(17/4) / 2 = 17/4 × 1/2 = 17/8
So, the rational number between 2 and 2 1/4 obtained by this method is 17/8.
Writing it as a mixed number, we can express it as:
17/8 = 2 + 1/8 = 2 1/8
Find a rational number with one decimal place that is between 17−−√ and 18−−√.
To find a rational number with one decimal place between √17 and √18, we can simply take the average of these two numbers:
(√17 + √18) / 2
Using a calculator, we evaluate this expression:
(√17 + √18) / 2 ≈ (4.123 + 4.243) / 2 ≈ 8.366 / 2 ≈ 4.183
Therefore, a rational number with one decimal place between √17 and √18 is approximately 4.2.
Which of the following is between π and 11−−√?(1 point)
Responses
10−−√
Start Root 10 End Root
7–√
Start Root 7 End Root
12−−√
Start Root 12 End Root
8–√
To determine which of the given options is between π and √11, we can compare their approximate values:
π ≈ 3.14
√11 ≈ 3.32
Checking the options:
- Option 10−√ is approximately sqrt(10) ≈ 3.16, which is between π and √11.
- Option √7 is approximately sqrt(7) ≈ 2.65, which is NOT between π and √11.
- Option 12−√ is approximately sqrt(12) ≈ 3.46, which is NOT between π and √11.
- Option √8 is approximately sqrt(8) ≈ 2.83, which is NOT between π and √11.
Therefore, the only option that is between π and √11 is 10−√.