Question

Which number produces an irrational number when added to 0.4

Answer 1

[AI-generated answer — Bot GPT 3.5]

An irrational number is any number that cannot be expressed as a fraction of two integers. So, any number that is not rational would produce an irrational number when added to 0.4. Some examples of irrational numbers are π (pi), √2 (square root of 2), or e (Euler's number).

Answer 2

Which number produces an irrational number when added to 0.4

√9

3 π

0.444...

2/7

Answer 3

[AI-generated answer — Bot GPT 3.5]

The number that produces an irrational number when added to 0.4 is √9.

√9 is equal to 3, which is a rational number. Adding a rational number to 0.4 would still result in a rational number. Therefore, √9 does not produce an irrational number when added to 0.4.

Answer 4

Which of the following statements is true if p is an integer and q is a nonzero integer?

A rational number can be written as a fraction

all numbers can be written as a fraction

an irrational number can be written as a fraction

a rational number cannot be written as a fraction

Answer 5

[AI-generated answer — Bot GPT 3.5]

The correct statement is: A rational number can be written as a fraction.

Answer 6

Which number produces an irrational number when multiplied by 1/3

0.166

-√17

2/3

2

Answer 7

[AI-generated answer — Bot GPT 3.5]

The number that produces an irrational number when multiplied by 1/3 is -√17.

√17 is an irrational number since it cannot be expressed as a fraction. When multiplied by the rational number 1/3, the result is still irrational. Therefore, -√17 produces an irrational number when multiplied by 1/3.

Answer 8

True or False:

The number 0.3333... repeats forever; therefore, it is irrational.

Answer 9

[AI-generated answer — Bot GPT 3.5]

False. The number 0.3333... is a repeating decimal, but it is still rational. It can be expressed as the fraction 1/3, which means it is a quotient of two integers.

Answer 10

Which number is irrational?

√5

0.3

0.777...

0.454545...

Answer 11

[AI-generated answer — Bot GPT 3.5]

The number that is irrational is √5.

√5 is the square root of 5, and it cannot be expressed as a fraction or terminating decimal. Therefore, √5 is an irrational number.

0.3, 0.777..., and 0.454545... are all rational numbers as they can be expressed as fractions or terminating decimals.

Answer 12

Which number is rational?

0.333...

0.83587643

π

√7

Answer 13

[AI-generated answer — Bot GPT 3.5]

The number that is rational is 0.83587643.

A rational number is one that can be expressed as a fraction of two integers. 0.83587643 can be expressed as a fraction since it terminates, making it a rational number.

0.333... is a repeating decimal, but it can be expressed as a fraction of 1/3. Therefore, it is also rational.

π (pi) and √7 (square root of 7) are both irrational numbers as they cannot be expressed as fractions of two integers.

Answer 14

Which number produces a rational number when multiplied by 0.5?

√3

-1.73205089

1/3

0.54732814

Answer 15

[AI-generated answer — Bot GPT 3.5]

The number that produces a rational number when multiplied by 0.5 is 1/3.

Multiplying 1/3 by 0.5 gives us 1/6, which is a rational number.

√3 and -1.73205089 are both irrational numbers, and multiplying them by 0.5 would still result in irrational numbers.

0.54732814 is a rational number, but when multiplied by 0.5, it results in a decimal that is not exactly representable as a fraction. Therefore, it does not produce a rational number when multiplied by 0.5.

Answer 16

Which number produces a rational number when added to 1/5?

- 2/3

√11

π

-1.41421356

Answer 17

[AI-generated answer — Bot GPT 3.5]

The number that produces a rational number when added to 1/5 is -2/3.

When you add -2/3 to 1/5, you get (-2/3) + (1/5) = ( -10/15 ) + ( 3/15 ) = -7/15, which is a rational number.

√11, π, and -1.41421356 are all irrational numbers, and adding them to 1/5 would result in irrational numbers.

Answer 18

True or false:

The number 0.8 can be written as 8/10, so it is an irrational number.

Answer 19

[AI-generated answer — Bot GPT 3.5]

False. The number 0.8 can indeed be written as 8/10, but it is still a rational number. A rational number is any number that can be expressed as a fraction of two integers, and 8/10 satisfies that condition.