What is a rational number with a denominator of 7 that is between √11 and √12. Write your answer as an improper fraction
To find a rational number with a denominator of 7 between √11 and √12, we need to determine which perfect square roots fall in between these two values.
√11 ≈ 3.316
√12 ≈ 3.464
Since 3.316 < √11 < √12 < 3.464, we know that the rational number will be closer to √11.
To find the exact rational number, we need to determine which fraction with a denominator of 7 is closest to √11.
Multiplying both sides of the inequality by √7 produces:
3.316√7 < √77 < 3.464√7
Now, let's simplify these values further:
3.316√7 ≈ 3.316 × 2.646 ≈ 8.763
√77 ≈ 2.646 × 2.646 ≈ 6.98
3.464√7 ≈ 3.464 × 2.646 ≈ 9.151
From the above calculations, we see that 8.763 < √77 < 9.151. Thus, the rational number we are searching for is between 8.763 and 9.151.
To convert this number into an improper fraction with a denominator of 7, we need to find the nearest integer.
The nearest integer to 8.763 is 9, and the nearest integer to 9.151 is also 9.
Therefore, a rational number with a denominator of 7 that is between √11 and √12 is 9/7.
What is a rational number with a denominator of 7 that is between √11 and √12. Write your answer as an improper fraction
21/7
22/7
23/7
24/7
25/7
To find a rational number with a denominator of 7 that is between √11 and √12, we need to determine which fraction is closest to these square roots.
Recall that √11 ≈ 3.316 and √12 ≈ 3.464.
First, let's convert these square roots into fractions with a denominator of 7:
√11 ≈ 3.316 ≈ 3 and 4/7
√12 ≈ 3.464 ≈ 3 and 5/7
We see that √11 is closest to 3 and 4/7, and √12 is closest to 3 and 5/7.
Therefore, the rational number with a denominator of 7 that is between √11 and √12 is 23/7.
Which is an integer but is not a whole number?
0
3/5
8
-0.7
-4
An integer is a number that can be positive, negative, or zero, and does not have any fractional or decimal parts. A whole number, on the other hand, is a non-negative integer.
From the given options:
- Option 0 is an integer and a whole number since it is non-negative.
- Option 3/5 is not an integer since it has a fractional part.
- Option 8 is an integer and a whole number since it is non-negative.
- Option -0.7 is not an integer since it has a decimal part.
- Option -4 is an integer since it represents a negative whole number.
Therefore, the answer is:
3/5
Which is a terminating rational number?
1 point
-1/3
√11
- 0.0716
0.51515151...
A terminating rational number is a rational number that can be written as a fraction in the form of p/q, where p and q are integers and q ≠ 0, and the decimal representation of the number terminates, meaning it has a finite number of digits after the decimal point.
From the given options:
1 point - This is not a number, but a phrase that is commonly used to indicate a score or a measurement. It cannot be classified as a number.
-1/3 - This is a rational number, but its decimal representation does not terminate; it repeats infinitely. It can be written as -0.333... with the 3s repeating.
√11 - The square root of 11 is an irrational number, meaning its decimal representation is non-terminating and non-repeating. It cannot be written as a fraction in the form of p/q.
-0.0716 - This is a rational number, and its decimal representation terminates after four digits. It can be written as -716/10000, which can be simplified as -179/2500.
0.51515151... - This is a rational number, and its decimal representation repeats the pattern '51' infinitely. It can be written as 51/99, which can be simplified to 17/33.
Therefore, the terminating rational number is -0.0716.