QuestionIdentify the true statement:
1. $\sqrt{2}$ is an integer.
2. 0 is neither rational nor irrational.
3. $4.8 \overline{33}$ is rational but not an integer.
4. -6.175 is irrational.

Studdy Solution

STEP 1

Assumptions1. We understand the definitions of integer, rational number, and irrational number. . An integer is a number that can be written without a fractional component.
3. A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero.
4. An irrational number is a number that cannot be expressed as a ratio of two integers.

STEP 2

First, let's evaluate the statement " $\sqrt{2}$ is an integer". The square root of2 is a number which when multiplied by itself gives the product2.

STEP 3

Calculate the square root of2.
$\sqrt{2} \approx1.41421356$

STEP 4

Since $\sqrt{2}$ is not an integer, the statement " $\sqrt{2}$ is an integer" is false.

STEP 5

Next, let's evaluate the statement "0 is neither a rational number nor an irrational number". By definition, a rational number is a number that can be expressed as a fraction p/q where p and q are integers and q is not equal to zero.

STEP 6

0 can be expressed as the fraction0/1, where0 and1 are integers and1 is not equal to zero.

STEP 7

Since0 can be expressed as a fraction, it is a rational number. Therefore, the statement "0 is neither a rational number nor an irrational number" is false.

STEP 8

Next, let's evaluate the statement " $4.8 \overline{33}$ is a rational number but not an integer". The number $4.8 \overline{33}$ is a repeating decimal, which can be expressed as a fraction, thus it is a rational number.

STEP 9

However, $4.8 \overline{33}$ is not an integer because it has a fractional part. Therefore, the statement " $4.8 \overline{33}$ is a rational number but not an integer" is true.

STEP 10

Finally, let's evaluate the statement "-6.175 is an irrational number". The number -6.175 can be expressed as a fraction -6175/1000, where -6175 and1000 are integers and1000 is not equal to zero.

STEP 11

Since -6.175 can be expressed as a fraction, it is a rational number, not an irrational number. Therefore, the statement "-6.175 is an irrational number" is false.
The only true statement is " $4.8 \overline{33}$ is a rational number but not an integer".

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QuestionIdentify the true statement:
1. $\sqrt{2}$ is an integer.
2. 0 is neither rational nor irrational.
3. $4.8 \overline{33}$ is rational but not an integer.
4. -6.175 is irrational.

Studdy Solution

STEP 1

STEP 2

First, let's evaluate the statement " $\sqrt{2}$ is an integer". The square root of2 is a number which when multiplied by itself gives the product2.

STEP 3

Calculate the square root of2.
$\sqrt{2} \approx1.41421356$

STEP 4

Since $\sqrt{2}$ is not an integer, the statement " $\sqrt{2}$ is an integer" is false.

STEP 5

Next, let's evaluate the statement "0 is neither a rational number nor an irrational number". By definition, a rational number is a number that can be expressed as a fraction p/q where p and q are integers and q is not equal to zero.

STEP 6

0 can be expressed as the fraction0/1, where0 and1 are integers and1 is not equal to zero.

STEP 7

Since0 can be expressed as a fraction, it is a rational number. Therefore, the statement "0 is neither a rational number nor an irrational number" is false.

STEP 8

Next, let's evaluate the statement " $4.8 \overline{33}$ is a rational number but not an integer". The number $4.8 \overline{33}$ is a repeating decimal, which can be expressed as a fraction, thus it is a rational number.

STEP 9

However, $4.8 \overline{33}$ is not an integer because it has a fractional part. Therefore, the statement " $4.8 \overline{33}$ is a rational number but not an integer" is true.

STEP 10

Finally, let's evaluate the statement "-6.175 is an irrational number". The number -6.175 can be expressed as a fraction -6175/1000, where -6175 and1000 are integers and1000 is not equal to zero.

STEP 11

Since -6.175 can be expressed as a fraction, it is a rational number, not an irrational number. Therefore, the statement "-6.175 is an irrational number" is false.
The only true statement is " $4.8 \overline{33}$ is a rational number but not an integer".

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QuestionIdentify the true statement: 1. 2\sqrt{2}2​ is an integer. 2. 0 is neither rational nor irrational. 3. 4.833‾4.8 \overline{33}4.833 is rational but not an integer. 4. -6.175 is irrational.

Studdy Solution

STEP 1

STEP 2

First, let's evaluate the statement "2\sqrt{2}2​ is an integer". The square root of2 is a number which when multiplied by itself gives the product2.

STEP 3

Calculate the square root of2.2≈1.41421356\sqrt{2} \approx1.414213562​≈1.41421356

STEP 4

Since 2\sqrt{2}2​ is not an integer, the statement "2\sqrt{2}2​ is an integer" is false.

STEP 5

Next, let's evaluate the statement "0 is neither a rational number nor an irrational number". By definition, a rational number is a number that can be expressed as a fraction p/q where p and q are integers and q is not equal to zero.

STEP 6

0 can be expressed as the fraction0/1, where0 and1 are integers and1 is not equal to zero.

STEP 7

Since0 can be expressed as a fraction, it is a rational number. Therefore, the statement "0 is neither a rational number nor an irrational number" is false.

STEP 8

Next, let's evaluate the statement "4.833‾4.8 \overline{33}4.833 is a rational number but not an integer". The number 4.833‾4.8 \overline{33}4.833 is a repeating decimal, which can be expressed as a fraction, thus it is a rational number.

STEP 9

However, 4.833‾4.8 \overline{33}4.833 is not an integer because it has a fractional part. Therefore, the statement "4.833‾4.8 \overline{33}4.833 is a rational number but not an integer" is true.

STEP 10

Finally, let's evaluate the statement "-6.175 is an irrational number". The number -6.175 can be expressed as a fraction -6175/1000, where -6175 and1000 are integers and1000 is not equal to zero.

STEP 11

Since -6.175 can be expressed as a fraction, it is a rational number, not an irrational number. Therefore, the statement "-6.175 is an irrational number" is false.The only true statement is "4.833‾4.8 \overline{33}4.833 is a rational number but not an integer".

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIdentify the true statement:
1. $\sqrt{2}$ is an integer.
2. 0 is neither rational nor irrational.
3. $4.8 \overline{33}$ is rational but not an integer.
4. -6.175 is irrational.

First, let's evaluate the statement " $\sqrt{2}$ is an integer". The square root of2 is a number which when multiplied by itself gives the product2.

Calculate the square root of2.
$\sqrt{2} \approx1.41421356$

Since $\sqrt{2}$ is not an integer, the statement " $\sqrt{2}$ is an integer" is false.

Next, let's evaluate the statement " $4.8 \overline{33}$ is a rational number but not an integer". The number $4.8 \overline{33}$ is a repeating decimal, which can be expressed as a fraction, thus it is a rational number.

However, $4.8 \overline{33}$ is not an integer because it has a fractional part. Therefore, the statement " $4.8 \overline{33}$ is a rational number but not an integer" is true.

Since -6.175 can be expressed as a fraction, it is a rational number, not an irrational number. Therefore, the statement "-6.175 is an irrational number" is false.
The only true statement is " $4.8 \overline{33}$ is a rational number but not an integer".