identify which condition is necessary for a number to be rational

Question

it must not be an endless decimal
it must be written as a fraction.
it must be able to be expressed as an integer divided by a nonzero integer.
it must not be negative.

Answer 1

The necessary condition for a number to be rational is:

It must be able to be expressed as an integer divided by a nonzero integer.

This means that a rational number can be written in the form \( \frac{a}{b} \), where \( a \) is an integer and \( b \) is a nonzero integer. Rational numbers can include both positive and negative values, as well as whole numbers and fractions. The other options provided are either incorrect or not necessary conditions.

Answer 2

which of the following is irrational.

52.781654292
-7 8/37
~3/4
3.6363636363636363...

Answer 3

To identify which of the following numbers is irrational, we can analyze each one:

1. 52.781654292 - This is a decimal representation of a real number. Since it is finite and does not repeat, it is a rational number.

2. -7 8/37 - This is a mixed number, which can be expressed as a fraction (-7 + 8/37). Since it can be represented as a fraction (with an integer numerator and a non-zero integer denominator), it is a rational number.

3. ~3/4 - Assuming this denotes the fraction \( \frac{3}{4} \). Since this is clearly a fraction of two integers, it is also a rational number.

4. 3.6363636363636363... - This number is a repeating decimal (3.63 repeated). Any number that can be represented as a repeating decimal is rational.

Since all options listed are rational, we might interpret each and see if there has been a misunderstanding. All provided numbers are actually rational.

If you were asking for an irrational number not listed here, an example would be \( \sqrt{2} \) or \( \pi \). Would you like to provide more examples or clarify further?

Answer 4

estimate the value of 6 x ~2. which of the following choices is the best estimate?

6.4
7.1
9.8
8.4

Answer 5

To estimate the value of \( 6 \times \sqrt{2} \), we first need to estimate \( \sqrt{2} \).

The approximate value of \( \sqrt{2} \) is about 1.4.

Now we can multiply:

\[ 6 \times \sqrt{2} \approx 6 \times 1.4 = 8.4 \]

So the best estimate from the choices given is:

8.4.

Answer 6

which statement is true about the square root of 28?

it is between 5 and 6, probably closer to 6
it is between 5 and 6, probably closer to 5
it is between 6 and 6, probably closer to 6.
it is between 4 and 5, probably closer to 5.

Answer 7

To determine which statement is true about the square root of \(28\), we need to find where it lies between perfect squares.

The perfect squares around \(28\) are:

• \(5^2 = 25\)
• \(6^2 = 36\)

Since \(28\) is between \(25\) and \(36\), we know:

\[ 5 < \sqrt{28} < 6 \]

To further refine our estimate:

• The square of \(5.5\) is \(5.5^2 = 30.25\), which is greater than \(28\).
• The square of \(5.2\) is \(5.2^2 = 27.04\), which is less than \(28\).

Thus, \( \sqrt{28} \) is between \(5.2\) and \(5.5\), which means it is definitely closer to \(5.5\) than to \(5\).

Given this analysis, the correct statement is:

It is between 5 and 6, probably closer to 6.

Answer 8

which statement is true about the integer fraction that equals the square root of 2?

it requires a computer to find it.
it does not exist.
it is equal to 1.
it involves large numbers.

Answer 9

The correct statement about the integer fraction that equals the square root of 2 is:

It does not exist.

The square root of 2 is an irrational number, meaning it cannot be expressed as a simple fraction (i.e., it cannot be represented as \(\frac{a}{b}\) where \(a\) and \(b\) are integers). Therefore, no integer fraction equals the square root of 2. The other statements are incorrect regarding this property.