sing rational approximations, what statement is true?(1 point)

Question

3 > 9 3 > √9
π < 9 𝜋 < √9
3 < 9 3 < √9
π > 9 𝜋 > √9

Answer 1

To determine which statements are true, let's analyze each one in context.

1. 3 > 9: This statement is false.
2. 3 > √9: This statement is also false, because √9 = 3 and 3 is not greater than 3.
3. π < 9: This statement is true. The approximate value of π is about 3.14, which is less than 9.
4. π < √9: This statement is true as well because √9 = 3, and π (approximately 3.14) is greater than 3.
5. 3 < 9: This statement is true.
6. 3 < √9: This statement is false, as mentioned earlier.
7. π > 9: This statement is false.
8. π > √9: This statement is true because π (approximately 3.14) is greater than 3.

Therefore, the true statements are:

• π < 9
• 3 < 9
• π > √9

From the provided options, the true statements are:

• π < 9
• 3 < 9
• π > √9

Thus, the statement that is definitely true without ambiguity from your format is 3 < 9.

Answer 2

sing rational approximations, what statement is true?(1 point)
3 > √9
π < √9
3 < √9
π > √9

3 > 9 3 > √9
π < 9 𝜋 < √9
3 < 9 3 < √9
π > 9 𝜋 > √9

Answer 3

To determine which statements are true, let's analyze each option:

1. 3 > √9: This statement is false because √9 = 3, and 3 is not greater than 3.

2. π < √9: This statement is false, as √9 = 3, and π (approximately 3.14) is greater than 3.

3. 3 < √9: This statement is also false because √9 = 3, and 3 is not less than 3.

4. π > √9: This statement is true because π (approximately 3.14) is greater than 3.

Now, looking at the second set of options:

1. 3 > 9: This statement is false.

2. 3 > √9: This statement is also false (as stated before).

3. π < 9: This statement is true since π (approximately 3.14) is less than 9.

4. π < √9: This statement is false (as discussed earlier).

5. 3 < 9: This statement is true because 3 is less than 9.

6. 3 < √9: This statement is false (as stated earlier).

7. π > 9: This statement is false.

8. π > √9: This statement is true (as discussed earlier).

Summary of True Statements:

• From the first set, the true statement is π > √9.
• From the second set, the true statements are π < 9 and 3 < 9.

So the true statements from your options are:

1. π > √9
2. π < 9
3. 3 < 9

If you're looking for a single correct statement from the first group, the true statement is π > √9. If answering from the second group, either π < 9 or 3 < 9 is also correct.

Answer 4

only 1 can be correct

Answer 5

Understood! If only one statement can be correct, let's reassess the options closely and determine which one is definitively true:

1. 3 > √9: False (since √9 = 3)
2. π < √9: False (since π (approximately 3.14) is greater than 3)
3. 3 < √9: False (since 3 is not less than 3)
4. π > √9: True (since π is approximately 3.14, which is greater than 3)

The only true statement is:

• π > √9

So, the correct choice among the ones listed is π > √9. Thank you for your patience!

Answer 6

For a rational number to generate a repeating decimal, what must be true?(1 point)
The numerator must be an odd number.
The denominator must be a prime number.
The denominator must not evenly divide any power of 10.
The rational number must not be a mixed number.

Answer 7

For a rational number to generate a repeating decimal, the following must be true:

The denominator must not evenly divide any power of 10.

This is because a decimal will terminate if the only prime factors of the denominator (after simplification) are 2 and/or 5, which are the prime factors of 10. If there are any other prime factors in the denominator, the decimal representation will be repeating.

Thus, the correct answer is:

• The denominator must not evenly divide any power of 10.

Answer 8

A repeating decimal can be converted to what kind of number?(1 point)
an integer
an infinite decimal
an irrational number
a rational number

Answer 9

A repeating decimal can be converted to a rational number.

Repeating decimals are fractions in decimal form that do not terminate but have a repeating pattern, and they can always be expressed as a fraction of two integers, which defines rational numbers.

Thus, the correct answer is:

• a rational number.

Answer 10

When is it possible to find a rational number between two given rational numbers?(1 point)
It is possible only when the two given numbers are positive.
It is possible only when the two given numbers are integers.
It is always possible to find a rational number between any two rational numbers.
It is possible only when the difference between the two given numbers is at least 0.00001.

Answer 11

It is always possible to find a rational number between any two rational numbers.

The rational numbers are dense in the real numbers, which means that between any two rational numbers, no matter how close they are to each other, there exists another rational number. For example, if you have two rational numbers \(a\) and \(b\) (where \(a < b\)), you can always find a rational number such as \(\frac{a + b}{2}\) which is the average of the two.

Thus, the correct answer is:

• It is always possible to find a rational number between any two rational numbers.