Which set of numbers is always rational?(1 point)

Responses

integers
integers

positive numbers
positive numbers

decimals
decimals

negative numbers
negative numbers

integers

Using a number line, what whole number and rational number to the nearest half is 20−−√

between?(1 point)
20−−√ is between

and

20−−√ is between 4 and 5.

Write 1,357 in expanded form.

1,000 + 300 + 50 + 7

Write 1,357 in expanded form.(1 point)

Responses

(7 x 1,000) + (5 x 100) + (3 x 10) + (1 x 1)
(7 x 1,000) + (5 x 100) + (3 x 10) + (1 x 1)

(3 x 100) + (5 x 10) + (7 x 1)
(3 x 100) + (5 x 10) + (7 x 1)

(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)
(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)

(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)
(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)

(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)

Which of the following is an irrational number between 8 and 10?(1 point)

Responses

62−−√
square root of 62

120−−−√
square root of 120

50−−√
square root of 50

84−−√

square root of 62

Convert 0.18¯¯¯¯¯

to a rational number in simplest form.

To convert the repeating decimal 0.18¯¯¯¯¯ to a rational number, let's assign a variable to the repeating part.

Let x = 0.18¯¯¯¯¯

Multiply both sides of the equation by 100 to move the decimal point two places to the right:

100x = 18.18¯¯¯¯¯

Subtract the original equation from the new equation to eliminate the repeating part:

100x - x = 18.18¯¯¯¯¯ - 0.18¯¯¯¯¯
99x = 18

Divide both sides by 99 to solve for x:

x = 18/99

Simplifying the fraction, we get:

x = 2/11

Therefore, 0.18¯¯¯¯¯ = 2/11.

Using a number line, what whole number and rational number to the nearest half is 32−−√

between?(1 point)
Responses

between 5 and 5.5
between 5 and 5.5

between 6 and 6.5
between 6 and 6.5

between 5.5 and 6
between 5.5 and 6

between 6.5 and 7

32−−√ is between 5 and 5.5.

Convert 0.5¯¯¯

to a fraction.(1 point)
The fraction equivalent of 0.5¯¯¯ is

To convert the repeating decimal 0.5¯¯¯ to a fraction, let's assign a variable to the repeating part.

Let x = 0.5¯¯¯

Multiply both sides of the equation by 10 to move the decimal point to the right:

10x = 5.5¯¯¯

Subtract the original equation from the new equation to eliminate the repeating part:

10x - x = 5.5¯¯¯ - 0.5¯¯¯
9x = 5

Divide both sides by 9 to solve for x:

x = 5/9

Therefore, 0.5¯¯¯ = 5/9.

Determine for each number whether it is a rational or irrational number.(2 points)

Rational Irrational
1.3¯¯¯
Rational – 1 point repeating 3
Irrational – 1 point repeating 3
π2
Rational – pi over 2
Irrational – pi over 2
3–√
Rational – square root of 3
Irrational – square root of 3
5117
Rational – 5 and 1 over 17
Irrational – 5 and 1 over 17
−25−−√

1.3¯¯¯ is a rational number.

π^2 is an irrational number.
√3 is an irrational number.
5117 is a rational number.
-25−−√ is an irrational number.

Karissa says the number 17 is an irrational number. Which statement best explains whether Karissa is correct?(1 point)

Responses

Karissa is correct because 17 only has 2 factors.
Karissa is correct because 17 only has 2 factors.

Karissa is incorrect because 17 can be written as a fraction.
Karissa is incorrect because 17 can be written as a fraction.

Karissa is correct because 17 is not written as a fraction.
Karissa is correct because 17 is not written as a fraction.

Karissa is incorrect because 17 only has 2 factors.

Karissa is incorrect because 17 can be written as a fraction.

Which of the following rational numbers is between 5–√ and 10−−√

?

To find a rational number between 5−√ and 10−−√, we need to find a number that is greater than 5−√ but less than 10−−√.

One possible rational number between these two values is 7−√.

Which of the following rational numbers is between 5–√ and 10−−√

?(1 point)
Responses

2.5
2 point 5

3
3

16−−√
square root of 16

4–√

To find a rational number between 5−√ and 10−−√, we can simplify them as follows:

5−√ ≈ 5−2.236 ≈ 2.764
10−−√ ≈ 10−3.162 ≈ 6.838

Therefore, a rational number between 5−√ and 10−−√ is 3.