What situation describes opposite quantities that when combined would equal 0
5 answers
The situation that describes opposite quantities that when combined would equal 0 is called "cancellation" or "cancelling out". This situation occurs when two quantities have equal magnitudes but opposite signs. When these quantities are combined, their values subtract or cancel each other out, resulting in a total of 0.
Show an example of a rational number that is between √10 and √11.
To find a rational number between √10 and √11, we can take the average of these two numbers.
The square root of 10 is approximately 3.1623, and the square root of 11 is approximately 3.3166.
Taking the average of these two numbers, we get:
(3.1623 + 3.3166) / 2 ≈ 3.23945
Therefore, the rational number between √10 and √11 is approximately 3.23945.
The square root of 10 is approximately 3.1623, and the square root of 11 is approximately 3.3166.
Taking the average of these two numbers, we get:
(3.1623 + 3.3166) / 2 ≈ 3.23945
Therefore, the rational number between √10 and √11 is approximately 3.23945.
wait whats that in fraction form
To represent the rational number between √10 and √11 in fraction form, we can use a technique called rationalizing the denominator.
The decimal approximation we obtained for the number is 3.23945.
To convert it into a fraction, we need to express it as a ratio of two integers.
Let's assign the variable x to the rational number:
x = 3.23945
To eliminate the decimal, we can multiply both the numerator and denominator by 100000:
x = (3.23945 * 100000) / 100000
Simplifying, we have:
x = 323945 / 100000
This fraction can be further simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5:
x = (323945/5) / (100000/5)
Simplifying again, we get:
x = 64789/20000
Therefore, the rational number between √10 and √11 in fraction form is approximately 64789/20000.
The decimal approximation we obtained for the number is 3.23945.
To convert it into a fraction, we need to express it as a ratio of two integers.
Let's assign the variable x to the rational number:
x = 3.23945
To eliminate the decimal, we can multiply both the numerator and denominator by 100000:
x = (3.23945 * 100000) / 100000
Simplifying, we have:
x = 323945 / 100000
This fraction can be further simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5:
x = (323945/5) / (100000/5)
Simplifying again, we get:
x = 64789/20000
Therefore, the rational number between √10 and √11 in fraction form is approximately 64789/20000.
3 answers